To make the bow, you'll need three sticks and three strings. Arrange them like this, and you've got your bow. To craft an arrow, you'll need one flint, one stick, and one feather. Stack them up, and you get four arrows. You can hold a stack of 64 in each inventory slot.
To use the bow, you need to equip it and have arrows anywhere in your inventory. Hold down right click to charge and release to fire an arrow. Fully charged, your arrow will fly 24 blocks. Obviously, a bow is great for defending against skeletons, creepers, zombies or pigs. A fully charged arrow will do nine damage or ten on a critical hit. For reference, a creeper has 20 hit points.
If you miss your shot, your arrow will stay in the block it hits for 60 seconds where you can pick it up. This comes in handy when you're out exploring and running low on supplies. Note that arrows aren't great for endermen because each time it gets hit with an arrow, it will immediately teleport.