I taught Microbilogy lab a few times when I was a graduate student....a long time ago!
First off, bactreia are super small, so you need a high quality microscope with very high magnification, and an "oil immersion" lense (like 1000X !!!)....so that microscope in your kids science kit probably isn't going to cut it. Usually a "gram" stain will show up the basic things that are there....but you have lots of problems. First off, unless the water is heavily contaminated, you probably aren't going to even see anything at all....
The way water is tested, is it is run through a filter that catches the bacteria. The filter is then placed on a pad of growth media that soaks up through the filter, and the individual bacteria grow up into colonies. Different kinds of colonies will have different colors and shapes, and the tech can then stain them and look under the microscope to complete an identification.
At least this is how it was done back it the day. Now, it is possible to pop a sample in a mass spec (I have one of those that cost $500,000, to play with!) and get an identification in seconds!
And we haven't even talked about viruses (which you can't see and are very difficult to culture), or protozoa, and other things that would like to take up residence in your body.
The best practice in any outdoor/survival situation is to treat all water like it is contaminated!! If you have just sunk a new well or you are permanently locating at a water source, the best thing is to have it checked by an experienced professional. Also, have it checked for other contaminents like arsenic, etc.