How can I change component values in a premade circuit
Your question may end up getting removed as too broad, however, I'll give you a bit of direction.

For myself, I confine myself to working with circuits that I understand.  You can learn a lot and maintain your interest without going into high level math (calculus, linear algebra) but I think you will find you benefit massively from learning the low level math involved (basic electrical theory is mostly algebra and trigonometry) and working with simple circuits and moving to more complicated ones as you understand each one.  When I encounter design challenges that I don't yet have the math skills for or that I'm not familiar enough to deal with in reasonable time frame, I often resort to experimentation to get a short term answer.  I can calculate how fast my MOSFET is able to switch, but it will take me much less time to breadboard a voltage converter and put my cheap oscilloscope on it.  Past my oscilloscope's maximum frequency I have to go back to calculating.  I could calculate the frequency necessary to get a smooth DC output from my LC filter, but heck, it's already on a breadboard, why don't I just vary the frequency while I watch the oscilloscope?  

To get you started, I would suggest you learn(look up and make yourself a reference sheet):

Definitions of electrons and holes, charge(Avogadro's number, coulomb), voltage(volt), current(ampere), power(Watt/Horsepower)

Ohm's Law, Watt's Law

Formulas for series and parallel resistance

Kirchhoff's Laws

Edison 3 wire circuits

Relationship between DC and AC RMS voltage

Basic AC

Induction, transformers, AC motors/generators, DC motors/generators, Faraday's Law, 

Capacitance, power factor, power factor correction, RLC resonance

Formulas for series and parallel Induction and Capacitance

DC RLC circuits

AC RLC circuits

Semiconductors

I think if you work your way through this material, you will find by the end you should understand enough to do basic component upgrades and tweak resistors in circuits you understand, which will be a much larger category of circuits than it is now.

Edit: I just typed up a blurb on why you might be interested in spreadsheets and the internet ate it, so I'm going to have a bit of a break before I type it out again.  When I suggest you make yourself reference sheets as you study, I mean something like this math one or this physics one.  I stumbled upon them in ye local university bookstore and I was happy to part with a few maple dollars for well written all inclusive sheets, but even if you find something like them, writing out your own sheets as you learn things can be a great learning aid.