Bicycle Chain comes in many different ways.
Used for BMX, Single Speeds, Track and Fixed Gears. The chain is thicker because it doesn't need to bend to change gears. You will need a 1/8" chain breaker.
Remove the current chain using a chain tool. Examples. Place any link on the chain tool in the farthest slot away from the drilling thingy. The pin of the chain (the thing holding the links together) needs to be flush with the mandrel of the chain tool (the pushy thing that emerges when you tighten the chain tool).
Determine the length of your new chain by looping the chain around the largest cog and then the largest chain ring. Do NOT include the derailleur. The length determined by this method should be about one link shorter than the chain currently on the bike. (See video demonstration)