How to obtain bacteria samples at home?
First, and I cannot stress this enough, you should not go seeking out human pathogens if you don't have the appropriate equipment to handle it at the right safety level.  That goes for all pathogens, even ones you might find around your house.

In a professional lab, you might get samples from collaborators, clinical samples, vendor, or really an number of other professional resources.  A well respected vendor as an example is ATCC, but the general public wouldn't be able to "shop" there.

But you really don't need to go far to get a whole host of microbes to study, you can grow them all at your house.  The basics of bacteria culturing can really be broken down to three steps: (1) get a source of bacteria, (2) put some of the bacteria in an environment where they can grow easily, and (3) harvest them to do something useful with them. 

(1) Is fairly easy, bacteria are everywhere.  You can swab nearly any surface of anything in your house and come up with microbes (note you might also get some mold/fungi).  In this case (3) is easy as well.  Once you have culture you can streak it across a slide to view it under a microscope (you could also use several proper mounting techniques).  After all, looking at microbes under a microscope is the real goal here!

The only part of this plan that will take some real elbow grease is making your own culture dishes at home, but it's not as hard as you might think.



Making your own culture dishes:

1) The "plates" themselves.


  I recommend getting the smallest Tupperware like containers your can
  find that are microwave safe, dishwasher safe, and really make a good
  seal (water tight at the least). They really don't have to be big, and
  you will make your life easier if you buy a bunch to match. They need
  to be super clean. After running them through your dishwasher at home,
  put them all in a boiling pot of water until you are ready to pour in
  your "medium." A mid-low simmer will work


Note that you won't probably be able to have perfect sterile technique at your house, but you should try to do what you can.

2) Your "Medium" or Broth


  I highly recommend using pectin as your gelling agent if you can't get
  your hands on some agar. After that comes plain unflavored gelatin,
  but I recommend pectin. You can get it at almost any grocery store and
  my recipe is made assuming that. You can determine how much you want
  to make, just scale up the ratios. I'm going to list things as rough
  volume by volume so you won't need a scale.
  
  i) Make the powder first:
  
  
  45mL of pectin;
  4 bouillon cubes ground as finely as you can (you can get different
  types and results depending on if you start with vegetable, beef, or
  chicken. I recommend starting with vegetable.);
  125mL of refined white sugar;
  Additives (more on this later)
  
  
  ii) Mix the powder into 500mL of water.
  
  Before you mix in the powder, heat the water to 50-75oC (mid low heat), but not boiling. Mix the powder in while stirring until
  dissolved.
  
  iii) Bring the mixture up to a boil. Let it boil for about 2 min,
  stirring all the while.
  
  iv) Cover the pot and let it cool for 4-5 min.
  
  You by no means want it to cool down to room temperature, you just want
  to get it a little below boiling. If you are at 55oC or below it's
  definitely time move on.
  
  v) Dip/fill your "plates" 1/3 full of media using clean/sterile
  utensils and seal while hot but not boiling.
  
  You may have noticed this seems an awful lot like canning, and that's
  because it is. Again you want to be as clean as possible in this step
  and of course try not to burn yourself on anything.
  
  vi) Let your media plates set and chill over night in the
  refrigerator.
  
  You really probably only have to wait a few hours if you are anxious
  to get going. You are going to want to store the plates that you are
  not using in the refrigerator anyway. Also if you made a bunch of
  plates, let the cool on a counter before you put them in the fridge so
  that you don't raise the temp of your fridge too much.
  
  Remember the thing about additives? You can play around with adding
  different amounts and different types of salts, vitamins, food, or
  other items to see how they affect the cultures you get to grow. All
  kinds of fun there. First go round, leave them all out.




Now you have your own home made culture plates! The above recipe was empirically tested by my childhood, and repeated by my son's. Not all pectin from the store may be equal, this is with Ball Classic (I have no relation to the company). I'd love to know people's results in trying it, because I might need to re-think how/what I'm doing to get it to work.

Go around your house swabbing things with sterile swabs (you can get these at a drug store), and then streak them out on plate. While it will be a little different with a swab and homemade plate, the idea is similar to what is done here.

Leave your plate in a warm wet place, but not in direct sunlight. Ideal temp is going to be around 37, but you can leave them above and below that and still get things to grow. On top of our dryer is where I leave them.

After a day or so you should have colonies you can streak out on a slide and look under a scope. You will find all kinds of things this way. If you want a more formal way to put things on a slide, you can check out dry and wet mounting from a Google search.

You are actually quite likely to run into E.coli if you sample enough "areas" this way. Obviously don't eat or huff the stuff that ends up growing. Maybe you can post some fun pictures of this if you try it.

As pointed out in the comments, if you successfully get bacteria to grow, then you will need to successfully get rid of them.  I should point that a good set of rubber gloves (that you can bleach and wash after use), or disposable gloves are a really good idea when handling plates that have grown bacteria.



Clean Up



First off, I want to clearly say that this stuff can clog a pipe.  

If you tried to grow something on a plate, and you didn't get a colony that you can see with the naked eye (note some microbes might make CLEAR growths) you can probably just scoop the gel into the trash.

Note that I said probably.  If you swapped any part of your body, waste, or that of an animal you must decontaminate even if you didn't see anything grow.  On the plus side decontamination is easy.

If you did see something grow, or you otherwise need decontamination:

First make a 20% bleach solution in a large Tupperware like container (probably don't want to do this is a nice metal pot, but could do it in a junk one).  You can go as low as 10% bleach solution if you sure your bleach is NOT a cheap already watered down brand (like something bought at dollar store).  But just to be sure, I recommend 200mL of bleach in 800mL of plain tap water.

Drop your plates and lids into the bath (with the lid off) and let it sit for 10-15 min.  Then, working under/in the bleach solution with your gloves on, use a fork/spoon to get out the medium (it will be like thick jello).  Do this for all your plates, and you can do more than one at a time this way.

Once you have all the medium out and floating in the bleach, take the plates out and put them in the dishwasher.  Strain out the bleach/medium/funkiness you grew through a cheap colander (I recommend dishwasher safe plastic like PP).  Put what get's caught in the colander in the trash and take the trash out.  Wash the plates, lids, colander, and large container you used for the beach bath.

Slides

Slides present extra caution because they can break or shatter to create sharp edges.  For the most part, if you cover your sample with a cover slip, and seal it with nail polish, you can actually keep your slides indefinitely with little risk.  If you do decide to dispose of them, they should first go into a thick Ziploc bag (use an expensive freezer guard type bag for this) or into a Tupperware you don't mind throwing away.  If you never sealed your sample to your slide, you should also decontaminate the slide in bleach first (as above, with extra caution to not cut yourself).

If you are sophisticated enough to get microscopic photos of the microbes you see, by all means post them up and we'll try to ID them as best we can (many look very similar, and we use genetic or protein markers to get a true ID).