It's under the seat. It should be very easy to find after you have the seat off.
A small car battery is fine, as long as your leave the car OFF.
Did you leave the battery over the winter? If so, the capacity will likely be diminished, and you should replace the battery. A battery with diminished capacity is hard on your charging system and could leave you stranded. A new battery is much cheaper than a new charging system.
After the battery is charged, check the voltage with a voltmeter. If it's under 12.2V, get a new battery. Normal 12V batteries have 12.6V when fully charged.
The Battery Tender line of products are very reasonably priced and will prevent this problem from happening. If you store your bike next to an outlet, just plug it in during the winter. You'll get much more life out of a battery this way. It's much less annoying than running the bike every couple weeks.
EDIT: Mr. Dave is right about bump starting the bike. However, it's not particularly good for the bike.