A lot of people hybridize African Violets, Daylilies, Hostas, and many other plants that set seed really easily.

Hybridizing can be as simple as taking two plants and brushing the pollen from one on the stigma of the other to as complicated as keeping records for generations of plants in the effort to bring out one particular trait (like yellow african violets). With the former method, you usually won't get anything interesting, but it's still fun. With the latter, you have to be a bit more disciplined about choosing parents.

If you want to go all out, learn some basic mendelian genetics (people usually learn at least some of that in high school). Then you can learn about how (in general) hybridizers go about bringing certain traits out.

I'm planning to teach it to my kids once I get a little experience under my belt. :)

You might start with African violets. They have a long and complex hybridization history, so crossing any two varieties is likely to give you lots of seedlings with considerable variation. Some offspring may throw back to wilder types with what are considered undesirable characteristics (e.g., dropping flower petals after only a couple of days), but others will surprise you. I assume you have a diagram showing the reproductive parts of the flowers and can get pollen to the stigma. African violets have pollen sacs that often have to be cut open with a fine and sharp knife blade to get the pollen out. Once you have delivered pollen from one plant to the stigma of another, the ovary will swell up fairly dramatically. Wait a couple of months, and the ovary will turn brown and begin to split open. Harvest the abundant, dust-like seeds and set aside for a few days to let them dry. Then sow them at the surface of African violet mix and keep continuously moist till seemingly thousands of tiny seedlings appear. I keep the seedbed in a Zip-Loc or similar sealed plastic bag till I see sprouts and then prick out some of the plants for trnasplantation, as many as I can make room for. Keeping the seedlings in the bag after they sprout can lead to rot, so I remove them into the air and set them in a bright location out of direct sun. A north window is ideal.
Growing garden hybrids is trickier. Many cultivated plants from the local Home Depot or seeds from the large seed companies have been hybridized to produce the large, showy flowers many gardeners seek out. Many of these varieties will revert to a much less attractive wild type if hybridized. You could experiment with crossing different types and colors of petunia to start, since they are easy to cross and produce a lot of seeds quickly. From seed to blooming adult can take just eight weeks or less if you care for the seedlings properly. Give it all a try. I hybridize a type of succulent plant called Haworthia from South Africa and get some very cool plants when I achieve a successful cross between two different species.
biosparite

check this site out also
http://www.hcs.ohio-state.edu/hcs200/BreeLab.html

Hi

Basically you begin just before the flower fully opens, remove the petals and the anthers (which hold the pollen) and then put the pollen of your choosing on the pad of the stigma.

If you could tell us what type of plants you have available to work with, we should be able to offer more specific information.

Also, there might even be a forum dedicated to the plant or plants that you're interested in working with - GW Forum List

http://forums.gardenweb.com/forums/

Also, here's Max75 site given as a live link - Crop Breeding

But don't worry if the links embedded won't work, I guess that they don't work on all programs.

Marbree

Here is a link that might be useful: Google search on Hybridizing plants beginner

I'm only 12 and my parents homeschool me too. Hybridizing gives polynomials usefulness.

Daylilies are easy. My 6yr brother even does some crosses.
Squash is also easy. Find a flower with a baby fruit at the stem end. Then find one that doesn't have a fruit, pick it, peel off the petals, and twist it around on the pistil(the part on the inside of the fruited flower). Then leave it on the plant till the skin is hard and dry. At that point, my experience ends and you should go to the Seed saving forum to figure out how. Mark the flower or someone WILL pick it. The plant will not make many fruits once you have pollinated it.

Pumpkins are about the same, just bigger.Cukes are smaller. Try, if you want, crossing pumpkins and squash.
Billy

I'm going to try this with my canna lilies this year to see what I end up with. I've experimented with it in the past with my mothers tulips. I crossed her yellow and orange species (without her knowledge, I was still living at home at the time). She never figured out how she ended up with yellow tulips that had orange stripes on them and vice versa.