Visit a website with a virtual drum kit such as Drum Nuts or Ron Winter's Drum Kit. Many virtual drum kits feature a picture of a drum kit or pictures of individual drums.
Play drums by hitting letters on your keyboard. Each drum is usually assigned a letter that corresponds with a letter on your keyboard, and hitting that letter key or clicking the picture with your mouse will produce a drum sound.
Learn the different sounds for each drum. Learn the differences between the various drums---including kicks, snares and toms---and cymbals, which are usually high hats, rides and crashes.
Buy a program such as Reason, or if you have a Mac with iLife, you already have Garageband.
Buy a MIDI controller. You have many, many choices for MIDI controllers, from the tiny, minimalist Korg Nanokey to large, 88-key piano look-alikes, such as the M-Audio Keystation 88es. You will be able to get basic sounds with your mouse, but having a MIDI controller will exponentially expand your options.
Connect your MIDI controller to your computer using a USB cable. In many cases, your computer will recognize the MIDI controller; if not, visit the manufacturer's website for information about downloading drivers. If you're using a MIDI controller that does not have a USB port, you'll have to invest in a USB-to-MIDI cable, such as AudioLink made by Alesis.
Open Reason and go to Redrum, the simplest, most straightforward drum machine in Reason. If you're using Garageband, you can either open Loops or you can load a kit from Instruments.
Press the keys on your MIDI controller and use the mouse to play drum sounds.