I first did a little bit of research and found that herbs are quite easy to grow indoors as well as small tomato plants. I raided my mom's seed supply and planted 3 small plastic pots; tomato, basil, and coriander. I figured that coriander and basil would be handy in the winter for cooking and fresh tomatoes are always welcome in cold weather.
The plants have been growing for about a week now and the tomato and basil plants have already started to poke their little sprouts out. My coriander isn't faring as well though, no sprouts can be seen. I figure that I will wait a little longer before starting that pot over.
In this process I have learned a few rules regarding indoor gardening:
1) Plants must be kept in a well lighted area.
2) Don't water too much. This is a very basic rule, but I was overzealous at first and watered too much...my soil ended up molding.
3) Replant once plants start growing too large for the pot. I was quite excited to find out that replanting can be done in pretty much anything. No need for an expensive clay pot...use half of a milk jug with holes poked in the bottom.
Here are some pictures of my plants thus far, I'll re-post more as they continue to grow.