Many are asking what to do if they don't have a bandsaw. (In actuality, the bandsaw can be a tool that can spell the end of a bow...or more!...in a hurry if not used properly. However, it can also knock a bow out in a blazing hurry if used correctly.) SO...for those of you without a bandsaw, and for those not comfortable with its use, here's what I recommend to take the limbs down to thickness, cut the fades, and shape the handle.
I would assemble a tool kit consisting of a drawknife, Stanley Surfom rasp (or similar), a 4-in-1 rasp, a flat-bladed knife or cabinet scraper, sandpaper, steel wool, and a coping saw.
To take the limbs to thickness and rough out the fades, start with the drawknife, but TAKE IT SLOW! You can tear wood up in a hurry with a drawknife. When you get close to your taper lines, dig in with the Surform rasp. These things can take wood off in a hurry, but do so in a much more controlled manner. They will leave behind a slightly gouged surface, so follow that up with your drawknife or flat-bladed knife used as a scraper, or a dedicated cabinet scraper. This is where you can true the belly up and make sure it doesn't have a crown (i.e. radius). Follow that up with some sandpaper (optional) and steel wool, and you're set!
Use the coping saw to rough out the handle. Then continue with the 4-in-1 rasp. Hit it with some sandpaper, and finally steel wool.
I also like to burnish the entire bow with a round piece of glass or metal to give it a nice appearance and keep inhibit splinters from raising on the back.
Hope this helps!