See the literature which came with your router for how to access its user setup screens. You'll need to note the default IP address of the router (usually in the range 192.168.0.1 though it varies by model). Connect the computer to the router with an ethernet cable. Open Internet Explorer and enter the router's IP address into browser's address bar as though it was a website.*
You should then reach the login page to the router's setup screens. The User name will probably be "admin" (without the quote marks) but the password can vary according to the brand of router **.
Once in to the router's setup screens, go to wireless security and review or renew the wireless security type and password. WPA PSK TKIP is the most common security type in use. Make a note of the SSID (the router's wireless call sign) or change it to one of your invention.
Go to wireless mode and ensure that it's set to n or g -- to match your computer's wireless adapter type (mixed mode is a safe bet).
Check for a setting often called Access List that includes or excludes users by identifying the MAC ID unique to their wireless adapter. Disable that.
Disconnect ethernet cable. Go to the computer's wireless networking setup screen and see if you can detect your router's SSID. Select that network. Apply the wireless security type and password to the computer's wireless networking setup screen.
* If there is no response from the router the default address may have been changed. So go Start then Run in XP - (Windows key plus R in Vista and Windows 7), then type in the following, including all the spaces:- cmd /k ipconfig /all -- then press Enter and from the black form that shows up, take a note of the numeric code beside the word "gateway" -- usually something like 192.168.0.1. Type exit to close the black form.
** The default password into the setup screens can be changed by the user. If this is blocking your access to the router setup screens, you may need to press the router's reset button (usually behind a pinhole next to the ethernet sockets). Resetting will also restore the default IP address.