Bow Types
Compound
Compound bows can be easily identified by the gears at the top and bottom of the bow. These gears help to carry the weight of the bow when it is pulled all the way back. They are not as large as recurve bows, and are typically made of metal.
Recurve
Recurve bows are typically made of wood and are what people typically think of when they imagine archery. Recurves are large, and the correct recurve for you will be one that is a few inches taller than you are. Unlike compound bows, recurves do not help hold the weight of the draw.
Arrows
The kind of arrow heads you use will depend on what kind of archery you are doing. Target archery uses small tips, hunting uses broadheads, and there are even special Flu-Flu arrows for short distance shooting. Typical target arrows will have shafts made of carbon, and will have fletching (the 'feathers') made from plastic. Arrows can be very customized, and some people even make thair own.
Additional Gear
Releases
Releases are what you use to pull back and release the bow string. The two main ones are finger releases and mechanical releases. Finger releases are made of leather and protect your fingers from the string of the bow. Mechanical releases have a clip that attaches to the string, and a trigger is pulled to release the string.
Sights
A sight can be used to aim for different distances. Sights can have one pin or many pins. To set a sight, you practice at different distances, and change the location of the pin until it shows you where to aim for that distance.
Stabilizers
Stabilizers are plastic sticks that can be added to the front of the bow to help absorbe some the the shock of releasing an arrow. Stablizing the bow like this helps prevent you from accidently moving it while shooting, which would affect your shot.