I'm having trouble connecting my Linksys router to my comcast internet...?

I'm trying to connect my Linksys BEFSR81 router to my Thomson RCA DCM325 Cable Modem, I have successfully connected the router so that it receives a signal however it appears I can only connect one computer at a time to the ROUTER. I've reset the modem about 10 times(sometimes for 30 seconds and other times about 10 minutes). Maybe I'm retarded . Do I need a different router? Am I doing something wrong? Any help will be greatly appreciated.