Most computers, fresh from the electronics store, have a built-in sound card. This sound card will accept a microphone via a 1/8-inch mini jack. The jack will be pink, and the microphone cable will most likely be hard-wired to a small microphone intended for use with Skype or other voice-over-Internet applications. Although there is no reason you can't use these mics for recording music, particularly for special effects, their quality will generally be optimized for spoken-voice use.
Using a professional microphone on a computer with 1/8-inch sound-card jacks is possible. There are XLR-to-1/8-inch adapters, but these are usually meant for video applications and have stereo mini-plugs. Easier to find and more appropriate to this application is a double-adapter setup with an XLR-to-1/4-inch mono phone plug, then a 1/4-inch-to-1/8-inch mono mini-plug. This will get your microphone signal to the computer but will lose the noise-canceling properties of a balanced XLR cable. Keep cable length as short as possible to minimize noise.
To take full advantage of balanced XLR cables into a computer sound card, using a small audio mixer is the ideal solution. The mixer accepts the XLR cable and may even provide phantom power for use with condenser microphones. The mixer in turn will likely have an output option for RCA plugs. RCA-to-1/8-inch stereo mini-plug adapters are common and the mixer output is line-level, so this would be routed to the light blue line-in jack on the sound card.
USB 2.0 has become something of a standard to transmit audio back and forth between mics and computers. In fact, USB microphones are available now from many manufacturers. Other USB devices will provide one or more XLR inputs for connecting mic cables directly. Like a mixer solution, the low noise of the XLR cable is preserved, and often the analog-to-digital converters of the interface are of a higher quality than those built-in sound cards.