to AA!
Befofre setting up an aquarium, it's important you understand the nitrogen cycle and how to cycle your tank to make it safe for fish. Doing so is the number one key to running a healthy aquarium. Here are some helpful links:
The Aquarium Nitrogen Cycle
Guide to Starting a Freshwater Aquarium - Aquarium Advice
The (almost) Complete Guide and FAQ to Fishless Cycling - Aquarium Advice
There are some options out there for a 10 gal tank, but know that the majority of fish you see in the average pet store are not good candidates for a tank this size. In general, you want fish that do not exceed 2" and have an appropriate activity level.
Nano fish are perfect for smaller tanks like this, but may not be available to you if you are not able to shop online, depending on your local selection. Some nanos to keep an eye out for are chili rasbora, celestial pearl danios/galaxy rasboras, ember tetras, pygmy or dwarf cories (pygmaeus and habrosus cories), sparkling gourami, and scarlet badis.
Of the common easy to find fish, the ones that come to mind at the moment for a 10 gal are guppies, platties, pork chop rasbora, neon tetra, and marble hatchets. Take a look at these and see if you're interested in any of them. Take note of any others that you like as well, and then ask here about them. Once you know exactly what you want, you can start looking at the specific numbers of them you should stock. It's impossible to say how many fish should be stocked w/o knowing the specific species you would like.