Philmont,
Don't get me started talking about plant breeding. I might not stop.
But seriously, interbreeding plants is something that anyone can do. Don't be afraid to jump right in.
In a nutshell, interbreeding plants involves putting pollen from the intended male parent plant onto the female parts of the intended female plant (many plants can be used as either the male or the female). Then, the resulting seeds need to be grown. These will be the offspring of the two parent plants.

For more detailed descriptions of the process, try searching the internet for specific plants in combination with the word hybridizing (or breeding).

Here's a good rose breeding link:
http://aggie-horticulture.tamu.edu/rose/rosebreeding/index.html

Here's a good daylily breeding link:

http://www.ofts.com/bill/hybrdize.html

I think that daylilies are a good one for beginners or children -- because they are so easy to work with. (And they're still a lot of fun for long time hybridizers.)

Good luck with whatever you decide to try. Let us know how things go. Tom