I will cover 4 simple survival bows you can make from typical materials found in either an urban or rural setting.
1) Stick bow
Just gather 3 sticks of equal length and relative thickness, less then 2 inches in diameter and 3 to 4 feet in length. Now remove all branches from the sticks. One of the three sticks should be about 2 to 3 inches longer then the rest, should be the thickest of the three is there is one. Now place them together and bind them in the middle with either sinew, paracord, shoe laises, dental floss, cordage from green strips of bark, vines, animal intestines, duck tape ect ect... Then bind them on the ends and between the ends and middle, should be 5 all together. Ensure that the wood is not gray or brittle, use partially but not completely dry sticks. Simple test, if they bend slightly then they are at least partially green, if they SNAP! then they aren't :) Now place slight notches in the middle longest stick sticking out of both ends and tie the bow string on. The bow string can be made out anything with the tinsel strength to do the job, nylon shoe laises tied together, cordage from dental floss, weaved cloth ect ect....
2)Fiber-glass bow
You may have noticed that some people have reflective rods at the border of their yards. These thin white rods the reflectives are on stuck in the ground are made of fiber glass, rubber coated metal or plastic. Fiber glass rods will make a stretching/breaking sound when you bend them. Get three of these and bind them in the middle, the ends and in between just as you would with the sticks or wrap the whole thing in duck tape with thicker binding points. Attach your bow string and your done. If you have more, you can make the bow have more thrust by adding 2 more rods or just use the extra rods as arrows, just attach fins and sharpen the end.
3)PVC bow
This is self explanatory, find a pvc pipe of no more then a 2 inch diameter between 3to 5 feet long and attach your cordage from one end to the other and your done.
4)Another simple bow is find a 2 inch diameter stick between 4 and 5 feet that is not gray or brittle and connect your cord between both ends.
These all are basic with limited range and a bow strength between 30-50 lbs of force which with a broadhead arrow can take down bigger game such as deer, have fun and be careful.
Remember that on any of these bows you may want to use cordage in the center of your bow to use as your arrow's rest.
To center your bow, just inch your finger down the inside spine of the bow balancing it on your finger. The point where the bow is balanced is the center.
If you use wooden dowel rods or straight dried sticks as your arrows with only a sharpened point, you can strengthen the point of the arrow by slightly burning the tip then filing the charred wood off with a rock. Your arrow tip will be alittle darker brown then the rest of the arrow and it will be harder because it is dryer then the rest. You can use plastic from bottles, feathers, leaves or cardboard to create fins for your arrows.