Diamonds are quite rare. They only spawn in the lower levels of the world. If you have a map go down to level 12 and start digging around and you will likely find diamonds. If you do not have a map then dig all the way down to bedrock and then go up 8 blocks.
Rule 1 with diamonds is to make sure you have a iron pick axe. If you try to mine a diamond block with anything else it will break the block, but it will not drop a diamond.
If you are digging very low, then you will likely come across lava at some stage. If you dig around the lava there is a good chance you will find some diamonds.
The most effecient method of finding diamonds (without cheating) is to strip mine. The video below will explain this process.