In addition to the already given answers, I've found a in-depth guide on how to build a bow (full credit goes to Jason Knight).
1. Choosing wood
The first step is to select the proper materials. Some of the best
woods for making bows include osage orange, yew, ash, black locust,
and hickory, though most hardwoods can work (other examples of
hardwoods include oak, maple, and beech).
For a quickie bow, you want to start with a relatively straight
section of sapling or branch that is free of knots, side branches, and
twists. You want this straight section to be about 5 feet long and
about 1.5 to 2 inches in diameter. Cut the sapling or branch carefully
so not to create cracks or splits in the wood. This is your bow stave.
2. Finding the belly, back, handhold, and limbs
Stand the bow stave upright on the ground, hold the top loosely with
one hand, and push outward lightly on the middle of the bow. The stave
will swivel to show you which way it is slightly curved. The outside
bend of the curve is called the "back" and the inside bend of the
curve is the "belly". Leave the "back" of the bow untouched. The back
receives the most tension and any damage to it can cause the bow to
break. This is one of the most important bow making instructions.
Now find the middle point of the stave and mark out your handhold area
by measuring and marking 3 inches out from the center in both
directions. The handhold area will also be left relatively untouched.
The area above the handhold is the upper limb and the area below is
the lower limb.
Now put the bottom tip of the bow on top of your foot and hold the top
tip while pushing outward from the belly side of the handhold. Only
push outward a few inches. Look at how the limbs bend. Observe which
areas bend and which areas do not. Begin removing wood with a knife
from the belly of the limbs where they do not bend while leaving
material in the areas of the limbs that bend a lot. Remember: only
remove wood from the belly side of the limbs, leave the back
untouched. The goal at this step in the process is to get the limbs to
bend evenly in the shape of a parabolic curve (like a satellite dish)
throughout their entire length.
Take off material slowly and re-check the bend of the limbs
frequently. The handhold and tips should stay straight or have very
little bend. You are ready for the next step of bow making
instructions once both limbs are no longer stiff and are able to flex
evenly throughout their length – thick staves will take lots of
carving, while narrow diameter staves may only need very little
4. Notches for the bow string
You can now carve small notches on the both sides of each tip, being
careful not to carve into the back of the bow. They only need to be
deep enough to keep a bow string in place. Tie loops into both ends of
a nylon, sinew, or plant fiber string, using a length that will allow
there to be 5 to 6 inches between the string and the handhold when the
bow is strung. String the bow; though be careful not to pull back on
the string yet (doing so can break the bow). Now you're ready for the
next bow making instructions.
Hang the bow up horizontally on a branch or piece of scrap wood by the
handhold. Now pull down a few inches on the string while observing how
the limbs bend. Now, not only do you want each limb to bend evenly
throughout its length, you also want each limb to bend exactly the
same amount (a mirror image of each other). Tillering is also one of
the most important bow making instructions.
Observe which limb bends less and carefully remove more materials from
the belly of that limb until both limbs bend equally and evenly.
Re-check frequently, pulling down on the string a little bit further
each time until you are able to pull it to your draw length (Your draw
length can be measured by imagining to hold a bow and pull the string
back to your upper jaw to a shooting position – the distance between
the handhold and your upper jaw is your draw length).
The tillering process is complete once both limbs flex equally and
evenly and the draw weight (pounds of pressure required to pull the
string back to a full draw) is at your desired poundage. A 25 to 35
pound draw is sufficient enough for hunting small game while 40 to 60
pounds is needed for larger animals like deer.
The poundage can be tested by placing a five foot 2x4 piece of lumber
vertically on a bathroom scale, then balancing the bow horizontally by
the handhold on top of the piece of lumber and pulling down on the
string to a full draw length. The scale will register the draw weight.
For wilderness survival situations the bow can now be used as is. Be
sure to never "dry" fire the bow (dry firing is when the string is
pulled back and let go without an arrow). This can break a bow. To
finish it off you can sand the belly smooth and oil it with a light
oil to prevent it from drying out too quickly. Many bowyers prefer
linseed or tung oil. To care for your bow, shoot it and oil it
frequently and adjust the tiller as needed. We hope you've found these
bow making instructions helpful. Enjoy!