Pretty simple; Hickory, elm, hop hornbeam, hackberry or locust if you don't have osage in your area, hickory or osage if you do. Cut at least a 6' long portion of the trunk for starters, be very aware of any cat eyes or places where the bark shows he tree has obviously grown over a dead limb. Pick a clean, no limbs or cat eyes, straight tree and you will be patting yours self on the back later when you start laying out your bow and have much more usable area to work from.
Seal the ends as soon as your trunk hits the ground with shellac, poly, wood glue or even a thick coat of rattle can spray paint. Split your trunk into quarters, pull the bark off if you can on white wood like those in the hickory, elm group mentioned above and seal the backs really well. I like shellac for backs, others use other sealers.
And that's about it, you have to stockpile wood to get started or buy staves from some other source.
I really recommend following Poorboy's board bow instructions(Google it) for the first few bows. A $6 oak board from Lowe's is an inexpensive way to start and will keep you busy while your wood stash is drying.