Software: Drivers and Programs
Here is where many people tend to get held up. The wired network is running just dandy, the wireless card isn't broken... so what's wrong? What else needs to be done to be able to connect to wifi?
Your first place to look will be the wifi software at its most basic: the driver information for the wireless card. For those who don't know, a driver is basically a piece of software that allows the hardware to interface correctly with the operating system of the computer. If your wireless card came with your computer, along with a preinstalled operating system, it should already have the driver information. However, if you've recently changed wireless cards, or have updated your computer, it could be that your wireless driver is no longer compatible with the operating system. Admittedly, this is more of a problem on older computers and on non-proprietary operating systems such as Linux, which may require some finagling.
Well, if it's not a driver issue, you have more potential problems to work through. Moving up the hierarchy, it could be that the software interface that you in turn use to work with the driver may have something wrong with it, perhaps a bug. While the software varies by your operating system, make sure that it is in the most stable up to date download.
Still not working? Well, it could be that the software isn't interfacing as desired with the wifi network. This could be because the wifi network is encrypted and you don't have the right key, in which case your only solutions are either to acquire the correct key or hack the encryption. The latter of the two options being quite technically complex, you'll probably just want to go with the former. It could also be that either the network administrator or the software on your computer are not correctly configured.
As you can tell, it's hard to be useful here without being specific to a given operating system! For more specific troubleshooting and diagnostic guides to any of the potential problems in connecting to wifi networks that I've outlined above, I'd recommend another search.