If it is a windows computer then when you run it for the first time it will guide you through a setup process which will include the step of connecting to existing wireless. On a mac you simply click on the airport, find your network, type password and connect.
Start by opening you network menu. Then select scan for networks. Select the network and click connect. If it is secured you will need to put in your network key. Once your done it should let you connect to the network.
If it is a desktop computer it's more likely that is doesn't have a wireless adapter and you will have to purchase one separately. If it's a laptop it should recognize the wireless right away. All you need to do is enter the password of your router and you should be ready to go.
Find the wireless network connection icon in the Taskbar, right click it, select "View Available Wireless Settings", double-click the wireless network you want to join, enter credentials, if applicable.