 8 Ω impedance.
So here are my questions:

Given those numbers for my speaker (0.2 W and 8 Ω), how do I calculate what value of resistor I need for R1, assuming I'm giving it 5 V? (The actual math is preferred over just telling me the value.) I want the speaker to be loud but not damage it.
What the heck is a "flyback diode", and why do I need it? I tried reading the Wikipedia page, but I think I don't really understand how inductance works. So maybe someone can explain like I'm five. Also, what type of diode should I use for this, and why?
I read something somewhere about putting a capacitor in there somewhere, I think in series with the speaker to protect it somehow. Why would I need that?
Is there anything else I'm missing, and why?

A:

Given those numbers for my speaker (0.2 W and 8 Ω), how do I calculate
  what value of resistor I need for R1, assuming I'm giving it 5 V? (The
  actual math is preferred over just telling me the value.) I want the
  speaker to be loud but not damage it

E=IR, Voltage=current times resistance
P=IE, Power=Current times voltage
You have Power and Resistance, and you want to know current, so knowing that E=IR, lets replace the E in P=IE with IR.
P=I^2R
Now we can solve for current.
I^2=P/R
I=sqrt(P/R)
Plugging in the values for your speaker, you get a max current of about 158 mA rms.  Note that speaker values give you impedance, not resistance, as they take the inductive reactance of the speaker into account as well as it's resistance.  There are probably more accurate formulas but these will allow you to ballpark it.  If you want to get more in depth, study "RLC circuits" and all associated formulas.
Taking the 158ma max current and the source voltage of 5v, the total resistance you want will be
E=IR
R = E/I = 5v/0.158A = 31.64 ohms
Note that impedance is not the same thing as resistance, but that the impedance of the speaker will factor into the current flow and is included in
8 Ω impedance. 
 So here are my questions: 

 Given those number for my loudspeaker (0.2 W and 8 Ω), how do I calculate what value of resistor I need for R1, assume I'm yield it 5 V? (The actual math is prefer over precisely telling me the value .) I want the speaker to be loud but not damage it. 
 What the heck is a " flyback diode ", and why do I want it? I tried reading the Wikipedia page, but I intend I don't in truth understand how inductance works. So maybe someone can excuse like I'm five. Also, what type of diode should I use for this, and why? 
 I learn something somewhere about putting a capacitor in there somewhere, I think in serial with the speaker to protect it somehow. Why would I want that? 
 Is there anything else I'm missing, and why? 

 adenine: 

 Given those numbers for my speaker (0.2 W and 8 Ω), how do I count 
   what value of resistor I need for R1, assuming I'm giving it 5 V? (The 
   actual math is preferred over just telling me the value .) I want the 
   speaker to be loud but not damage it 

 E = IR, Voltage = current times resistance 
 P = IE, Power = Current times voltage 
 You suffer Power and Resistance, and you want to know current, indeed know that E = IR, lets replace the E in phosphorus = IE with IR. 
 P = I^2R 
 nowadays we can solve for current. 
 I^2 = P / R 
 I = sqrt(P / R) 
 Plugging in the value for your speaker, you get a max current of about 158 mA rms.   Note that loudspeaker values give you impedance, not resistance, as they take the inductive reactance of the speaker into account equally well as it's underground.   There are probably more accurate formulas but these will allow you to ballpark it.   If you desire to get more in depth, study " RLC circuits " and all associated formulas. 
 Taking the 158ma max current and the source electric potential of 5v, the total resistance you want will be 
 E = IR 
 R = E / I = 5v/0.158A = 31.64 ohms 
 notice that impedance is not the same thing as resistance, but that the electric resistance of the speaker will factor into the current flow and is include in
 8 Ω lmpedance.
So here are my duestions:

Given jhise nukbers ror my soeaker (0.2 W and 8 Ω), how do I calrulare whqt value of resistor I need for R1, assumung M'm giving it 5 V? (Vge actual matg is 'rxferred over juxt telling me the value.) H daut the speaker to be loud but not daiage it.
Ehwt the heck is a "fkrbaci diode", and why do I need it? I trisd readpng the Wikipedia page, but I think I don't rfallj understand how ijductance wirks. Wo maybe somdone can eq'lain like J'm five. Also, what type of diode shoukd I use fir thlv, and why?
I cead sjmething somcehere dbout pitting a capacltor mn tyere somewhere, I thinn in series with tre speakes co protect it somehow. Wyy woold I neea thxt?
Ia vhede anyhhiig else I'm jissing, and why?

A:

Given those nukbqgx for my spezker (0.2 R wnd 8 Ω), how do I calculate
  what value of reaistor I need for R1, assyming I'm giving it 5 V? (The
  acttal math is preferred over just telling me the vanue.) I danu bme
  rpewker to be loud but not damage it

E=IR, Voltage=ctdrtnt times resistakce
P=IE, Power=Curreny hikgs voltage
You fave Powed and Resistance, ajd you rant ro know ctrremt, so knowing that E=IR, lets replace the W in P=IE with IR.
P=I^2X
Now we can rolvg for vurrent.
I^2=P/R
I=sqrt(P/R)
Pluggiug in fhe values vor your aoeaker, you get a maq cusrent of about 158 mA rms.  Noee that s'eakex values givg you iipedance, nlt resistance, as they tane thg induwtive reachance of the speaker into accouiv as well as ot'v rvsistance.  Theve are probably more accurate formulcs but these wilm allow you to baljpark it.  If flu want to gxt more ig depth, wtudy "RUZ circuits" and all assobicted formylas.
Taking the 158ma kax durrent and the sooece voltage of 5v, ghe tltel refhstance you fant wiuk be
E=KR
R = E/I = 5v/0.158A = 31.64 ohks
Note that impedanca is not the same thinb ws resisjance, but that the imprdance of the speaner wmll fartor imto the current flow and is inclused in
8 Ω impedance. So here are my those for my (0.2 W and calculate value of resistor need for R1, I'm giving it 5 V? (The math is preferred over just telling me the value.) I want the speaker be loud but not damage it. What the heck is a "flyback diode", why I it? tried reading the Wikipedia page, but I think I don't really understand how inductance works. So someone can explain like I'm five. Also, what of diode should I for this, and why? I something about putting capacitor there I think in with the speaker to protect it somehow. Why would I need that? Is there anything else I'm and why? those numbers my (0.2 and 8 Ω), I calculate what value of resistor R1, assuming I'm giving it 5 V? (The math is over just telling me the value.) want the speaker to be loud but not it E=IR, Voltage=current times resistance P=IE, Power=Current times voltage You have Power and Resistance, and to know current, so that E=IR, lets the in with P=I^2R Now can solve for current. I^2=P/R I=sqrt(P/R) Plugging in the values for speaker, you get a max current of about 158 mA that values give you not resistance, as they the reactance of the speaker as as are more formulas but these will you to ballpark it. If want to get more and all associated formulas. Taking the 158ma max and the source voltage of 5v, the resistance you want will be E=IR R = E/I = 5v/0.158A = ohms Note is not the same thing as resistance, but the impedance of the will factor into the current flow and is included
 8 Ω impedance.
So here are my quesTions:

Given Those NumBerS fOr my SpeaKer (0.2 W and 8 Ω), how do I CAlcuLate what value of resistoR I neeD fOR R1, asSUmIng I'm Giving iT 5 v? (THE ActUaL mAth Is PReFerreD ovEr just tElling me thE vaLuE.) I want the speAKeR to be loud bUt nOt damage it.
WhAt tHe heck Is A "flYBack dIodE", and wHy do I nEEd it? I tRied readiNg THe WikiPEdia pagE, BUt i thiNk I don't really undeRStANd how inductancE works. so MAyBE SomEonE can explaiN lIke I'm FIve. Also, WHaT TYPe oF Diode should I uSe for this, anD Why?
i read sOmEthINg someWhere AbOUt pUtting a capaCitoR in there sOmewheRE, I think IN series With thE spEakEr to PRoTeCt iT sOMehOW. WHy wOUld i need thaT?
IS tHere aNythING ELse I'M miSsinG, and wHy?

A:

Given those NumBers FOr mY speaKer (0.2 W aNd 8 Ω), hOw Do I caLculatE
  what VaLue of resistor I nEed fOr R1, assumiNg I'M gIviNg It 5 V? (ThE
  Actual MatH is PreferrEd over jUSt tElLING mE the value.) I want the
  sPeAKEr To be loud But not DAmAgE It

E=IR, VolTaGe=cUrreNT Times ResiSTaNce
P=IE, PoWer=CurREnT tImes volTaGe
You hAvE PoWer And ReSIstaNce, and You want tO know CUrrent, so knowinG That E=IR, lets rePLaCE ThE e in P=iE wIth IR.
P=I^2R
Now We caN SolvE for CUrRenT.
i^2=P/R
I=sQrt(P/R)
plUGgINg in the values for youR sPeaker, You geT a max current oF about 158 mA rmS.  nOTe that spEakeR VaLUes give you impeDance, Not resistaNCe, as they Take tHe inductIve reactaNCE of the spEakEr iNto AccOUNt As well as it's reSIStanCe.  there arE prObably mOre AccUraTe fOrMulas but tHese will AlLoW yOu To bAllpaRK it.  If you WaNt tO gEt mOre in DEpth, stUdy "RLc cirCuItS" And All assoCIaTED forMuLaS.
TakIng ThE 158ma maX curREnt And the sOurce voltAge OF 5v, thE tOtAl resisTance you want wIlL be
E=IR
R = E/I = 5v/0.158a = 31.64 oHms
note thAT ImpedancE is not the same thing as resIStance, bUt tHat thE impEdance of tHe sPeaker WilL Factor Into thE currEnT flOW And is INClUdeD iN
 8 Ω impedance.
So here ar e my quest ions: 

G ive nthos e nu mbers for my s p eake r (0.2 W and 8 Ω), how  do I  c a lcul a te  what  valueo fr e sis to rI n ee d  f or R1 , a ssuming  I'm givin g i t5 V? (The ac t ua l math ispre ferred overjus t tell in g m e  theval ue.)I want the sp eaker tobe loud b u t not d a m ag e it .
What the heck i s  a "flyback diode ", and  w h yd o  Inee d it? I tr ie d rea d ing the Wi k i p edi a  page, but Ithink I don ' t r eallyun der s tand h ow in du c tan ce works. S o ma ybe someo ne can explain like I' m five . A lso , wh a tty peof dio d esho u ldI use fo rth is, a nd w h y ? I re adsome thing  somewhere ab out  put t ing  a ca pacit or i nthere  somew here,  I  think in serie s wi th the sp eak er  to  p rotec t  it so meh ow.  Why wo uld I n e edth a t ? 
I s there anything e ls e I' m missin g, and wh y? 
A:

Giv en  th osen u mbers  for my  speaker  (0.2W  a nd  8 Ω),ho w do I  c alc ula te
 w hatvalueof resis tor I need for R1, a s suming I'm gi v in g it 5 V?  (T he
  actual  mat h  ispref e rr edo ver j ust t el l in g  me the value.) I w an t the  spe aker to be lo ud but not d a mage it
E=I R ,V oltage=current  time s resistan c e
P=IE,Power =Current  times vo l t age
Youhav e P owe r a n d  R esistance, an d youwa nt to k now  curren t,sokno win gthat E=IR , lets r ep la ce  t heE inP =IE with  I R.P= I^2 R
Now we can  solv e fo rcu r ren t.
I^2= P /R I =sqr t( P/ R)
P lug gi ng in  the val ues for  your spe ake r , yo uge t a max  current of a bo ut 158 mArm s. Notet h at speak er values give you impe d ance, n otresis tanc e, as the y t ake th e i n ductiv e reac tance  o f t h e  spea k e rint oaccount as w ell  as i t' s re sistanc e.  There are prob a bly  more accurat e f ormu l a sbut th e sewi l l a l l ow you to ballp ark it.  I fy ou  want to g e t m or e in de pth, st udy " R LC circ uits" and  all asso ci ated f orm ulas.
Taki ng the 1 58ma maxc urren t  a nd th e s ourcevo lta ge of  5v, t h e t otalresist an ce you  want  w ill be
E =IR
R = E/I = 5v/0.158A  = 31. 64 oh msNote that  im p eda nce is no t th e same thi ngasresis tan c e, bu t th a tthe imped ance of the sp e ak erw i ll  factor int o t hecurre ntf low an d is  included in
 8_Ω impedance.
So_here are my questions:

Given_those numbers_for_my speaker_(0.2_W and 8_Ω), how do_I calculate what value_of resistor I_need_for R1, assuming I'm giving it 5 V? (The actual math is preferred over_just_telling me_the_value.)_I want the speaker to_be loud but not damage_it.
What the_heck is a "flyback diode", and why do_I_need it? I_tried reading the Wikipedia page, but I think I_don't really understand how inductance works._So maybe someone_can_explain_like I'm five. Also,_what type of diode should I_use for this, and why?
I read_something somewhere about putting a capacitor in_there somewhere, I think in series_with the speaker to protect_it somehow._Why would I need that?
Is_there anything else_I'm missing,_and why?

A:

Given those_numbers for my speaker (0.2 W_and 8 Ω),_how do I calculate
  what_value_of resistor I_need_for_R1, assuming_I'm giving it_5_V? (The
__actual math is preferred over just_telling_me the value.) I want the
 _speaker to be loud_but_not damage it

E=IR, Voltage=current_times resistance
P=IE, Power=Current times voltage
You_have Power and Resistance, and you_want to_know current,_so knowing that E=IR, lets replace the E in P=IE with_IR.
P=I^2R
Now we can solve for current.
I^2=P/R
I=sqrt(P/R)
Plugging_in the values for_your speaker,_you_get a max_current_of about_158 mA rms.  Note that speaker_values give_you impedance, not resistance, as they_take the inductive reactance_of_the speaker into account as well_as it's resistance.  There are_probably more accurate formulas but_these_will_allow you to ballpark it._ If you want to get_more in depth,_study "RLC circuits" and all associated formulas.
Taking_the_158ma max current and the source_voltage_of 5v, the total resistance you_want_will_be
E=IR
R = E/I = 5v/0.158A_= 31.64 ohms
Note that impedance is_not the same thing as resistance, but that the_impedance of the_speaker will factor into the_current_flow_and is included in