This 'ible will vaguely teach you how to make a recurve bow.

Step 1: Step 1: Wood or Bamboo?

I would recommend either bamboo or tough, bendable wood, such as yew or hickory. They are very reliable and humans have been using them to make excellent bows for at least a millennia. Hickory and bamboo are generally more common worldwide than yew, because I've seen plenty of hickory and bamboo, just not as much yew. I've seen more bamboo than hickory, so go with bamboo, it is trustworthy and more common.

Step 2: Step 2: Single Piece or Multiple?

Definitely multiple, however, make them layers, not chunks. The Huns made their recurve a like that, and they made some of the best. So yeah, if you have time, go with layers.

Step 3: Step 3: Tools

Vice
Sandpaper
Moist cloth

Step 4: Step 4: Supplies

Strong wood glue
Bamboo planks
Strong, elastic string(preferably nylon)

Step 5: Step 5: Creation

When creating the bow, always taper the limbs to curve away at first, but curve back towards the front. Use the glue to plaster thin planks of bamboo or wood together. Make sure the handle is thicker than the rest of the bow, and that it fits in your hand nicely. Make the arrow rest so that the arrow can rest in an area closest to the exact middle of the bow, and make sure the arrow does not go to either side. After that is done, make sure the bow has not been strung, then put it in a cool, dry place to dry(have it dry about a year for best results if the wood or bamboo was fresh cut, or just have the glue dry properly). String it when when you want to shoot, and see how it handles! I would recommend the bow be about 3-4 feet long.