The SSID is the name of the network your router creates and if any of your computers is connecting wirelessly, it already knows that name.
If you aren't already using wireless, use the cable that came with your router to connect to your computer then go Start then Run in XP - or use the Windows key plus R in Vista and Windows 7, then type in the following into the Open box, 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 Default Gateway icon - 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 but your router's instruction manual will help you there.
The SSID will be shown under the WLAN settings heading and also the security key which the printer will have to know to be able to connect.