Diamonds are rare in Minecraft, but essential for crafting the most durable weapons and armor in the game. If you want to find diamond ore easily, you can use Mineviewer to help you.
First, download and unzip Mineviewer, then double click the .EXE file. You will then be asked to choose the world you want to view. Once you do this, a block of your Minecraft world will appear. You should recognize it as the place you last saved your game! I have pointed out the start of my mine below.
You can look around with the mouse, and move around with the cursor keys, or WASD. Click on the 'top' of the map, then use the comma and period keys to remove slices of the map:
Doing this, you'll see different color blocks on each slice (press K for a block key). Keep going far enough, and you will start to see the round blue blocks that signify diamond! They only exist really deep down, so you will have to mine a lot, but at least with Mineviewer you'll know where you're going...
If you're playing Minecraft on a Mac, try Minecraft X-Ray, which lets you search your world for ore in a similar way.