You need a digital audio workstation to record vocals. If you have an Apple computer, you should have access to Garage Band. If you have a Windows unit, you can download Audacity for free. I use Cakewalk Sonar 8 Producer Edition (pictured above).
Your most obvious tool. If you're serious about recording vocals you're going to need to spend at least $200, but there are less expensive options. I use the Audio Technica AT4050 (pictured above).
You need an audio interface to plug everything together. You will run your monitors, microphones and instruments through the interface. I use the M-Audio Profire 610 (pictured above).
You should also think about investing in microphone accessories that will help make your vocals more crisp and clear. Two of the most common used tools for this very purpose are the VoxGuard and the Pop Filter. The VoxGaurd (pictured above) acts as a small room for the mic, helping to lessen outside and ambient noise, like the type your computer fan makes.