If your apartment complex offers wireless service, all you need to get set up is;
-A Wireless capable computer. Most laptops nowadays come with a wireless card in them. If you have a desktop, you may need to purchase a internal or an easier to use USB model that will allow you to access wireless networks.
-The security key from the admin of the router. This is what you will input as the "password or passphrase" when connecting to the network to gain access to it.
Other than those two things you should be good to go. Just talk to the complex or whoever is in charge of the internet access and see if you can obtain the security key, and for help actually setting it up if you need to be shown how in order to remember how to do it. Once you do it, it's fairly simple and easy to remember.
If you have any other questions about this, feel free to ask away.