On your the other computer, first follow the instructions manual
to install the wireless drivers properly. Usually plug and play
would work, but if it doesn't, there should be a CD that you can
insert and install.
After that, reboot.
Next, on your computer, log in to the router. Look around the
settings and find the wireless settings.
Wireless network name is usually called SSID. If you find such a
field, enter a wireless network name for your wireless network.
Give it a unique name so it won't clash with your neighbours and
cause you to lose connections, lose signal strength or even to the
extent of not able to connect due to different security
settings.
After that, navigate around to find the wireless security
settings. Some routers put them together with the wireless settings
page, some put it in the advanced page.
If both computers are using XP, I will recommend you to use WPA.
When selecting WPA, please choose the Pre-shared Key (PSK) option.
The other options will require a server.
For the PSK field, treat it as a normal password field and enter
a password. Write it down somewhere because you will need it.
If both computers are using Vista, you can set it to use WPA2,
which is more secure than WPA. Again, you should choose the PSK
option.
After that, save the settings and restart the router (if
necessary).
Once that is done, try connecting to your wireless network.
Enter the PSK that you've written earlier and set it to remember so
you don't have to always re-enter it.