If you had nothing but a survival knife or hatchet, could you make a hunting bow that works? The guy from BushCraftMyWay has it figured out. You'll need a survival knife or a hatchet, and if you want to fire harden your bow, you'll obviously need to know how to make a fire.
Step 1) Find a stick or branch, preferably one with a natural curve
Step 2) Remove the bark
Step 3) Use your knife or hatchet to cut of imperfections such as knots
Step 4) Fire harden your bow (optional) This will add about 10 pounds of strength to your bow.
Fire hardening your bow is not difficult. Rotate the wood over the flames until it becomes golden brown. Don't allow your stick to catch on fire though.