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If you want to be strictly trad, look into selfbows i.e no backing - just the stick. This requires you to peel the stave down to a single growthring along the back or you'll introduce weakspots. Then also get linen thread for a string, quills for arrow flights, look into creating hide glue or fish glue etc. I'd keep it simple to begin with though.
The process steps in order are:
Cure wood
Hew out rough bow outline
Drawknife or rasp to refine shape
Establish a nice back, either a single growthring or prepare the surface for a backing material by rasping or similar.
Glue on backingmaterial
Let dry for a few weeks ideally, to let the glue dry and the moisture totally leave both rawhide and wood. Make a tillering stick, string and arrows at this time. Make the string very long so you can use it while tillering, you can cut it down for final use when tillering is done.
Remove excess rawhide, cut nocks and shape the handle. Keep in mind nock notches should be at an angle as the string doesn't point away from the limbs perpendicularly.
Begin carefully removing material off the "belly" side of the limbs while "floor tillering" (just bending the limbs against the floor with your bodyweight) occasionally to make sure they bend somewhat evenly.
Attach string and begin tillering using tillering stick.
When tillering is done, do the final cosmetic work and seal the wood with lacquer or similar. Rawhide doesn't respond well to oil, but half-matte lacquer looks pretty good.
