People frequently ask this question and the answer is in the router's settings pages. Here's how to find those and find or alter the information you need. Firstly, and with thanks to WR2 for reminding me, some routers have the relevant information printed on a sticker somewhere on the casing. If yours does not, try this:-
Connect your router to a computer with the cable that came with the router then go Start then Run in XP or press the Windows key and R together in Vista and Windows 7, then type in the following, including all the spaces:-
cmd /k ipconfig /all
press Enter and from the black form that shows up, take a note of the numeric code beside Default Gateway - something like 192.168.0.1.
Type exit to close the black form.
Open Internet Explorer and enter that code into the URL address bar as though it was a website. You're then at the login page to the router's settings utility and admin will usually be the login with either admin or password as the password. If neither work, go back to the manual or to the router maker's website.
If you're in, seek out Wireless and then Security and take a note of the key. Sometimes it may be a passphrase, some a simple set of letters and others a hexadecimal code. You also may as well note which level of security it is - WEP, WPA or WPA/PSK 2 and then either AES or TKIP. Your computer will already know this but it's handy information to store. Note also that hexadecimal only contains numbers from zero to 9 and letters a to f so there's no confusion of I and O with 1 and 0.
The best and most secure level of security is WPA2 so go for that one if you have a choice.
It's best to keep a note of that security key in your Documents folder and also outside the computer.