Determine whether or not your sound card will require an external power supply in order to run the condenser microphone. All condenser microphones require 48 volts of power, typically referred to as "phantom power." If you are using an external sound card with an XLR input (the professional standard for microphones), then it is likely that the sound card can supply this power to the microphone. Just look for a switch or button that says "+48V" or something similar, and activate it. If your sound card does not have a built-in phantom power supply, you will need to either purchase another sound card that does, or purchase an external phantom power supply.
Plug one end of the cable into the microphone and the other end into the sound card. If you are using your computer's built-in sound card instead of an external one, then your only microphone input is probably a 1/8 inch jack. In this case, an audio adapter may be necessary to convert the microphone cable's XLR or 1/4 inch plug to a 1/8 inch plug. These adapters are quite inexpensive and are readily available at most music and electronics stores.
Test the microphone by speaking into it. You may need to access your operating system's audio properties to unmute the microphone and adjust its volume. The details of this process will differ depending on the operating system you use, but the basic idea is to simply make sure the microphone is being properly routed into the sound card and out of the speakers. Once that happens, the microphone is hooked up to the computer and is ready for live performance, recording, or adding effects.