Search the DIY forum, this topic comes up there all the time.
But here's a quick recap. You'll need fan(s) and a power supply, of course. Most computer fans are 12VDC, so your power supply needs to supply 12VDC. This is a common size for wall warts.
In order to buy the correct power supply, you also need to know the current that your fans will draw. It's provided in the specs for most fans - if in doubt, assuming half an amp is probably safe, unless you have some monster fans. Add up the current draws for all your fans, and then make sure that your power supply has a current rating that's MORE than this value. If you run the power supply at or above the rated current draw, you'll cook it (or possibly start a fire.)
If you are wiring one fan, simply splice it to the wires coming out of the power supply. If you are wiring multiples, you need to wire them in parallel - that is, all of the + leads from the fan together to the + on the supply, and all of the - leads to the - on the supply.
To make the actual connections, use your favorite safe method. Wire nuts are OK - fill them with silicone or heatshrink them to make them less susceptible to failure. Crimped butt joints would work too, again heatshrinked if they don't have heatshrink built in. Soldered connections are great if you can pull it off - if you aren't sure of your soldering skills, just use the crimped connectors.