[opensuse] SSH Over LAN Problem

My problem is that I don't know how to do that. I have ssh (OpenSuSE 11.0) working over the Internet so the installation appears to be ok. I've gone to several SSH howto sites but come out more confused than I went in. It seems to me that there should be a simple ssh command to allow me to connect to another machine on my LAN, something like: ssh -l alice Venus-ws.homeoffice Am I essentially correct or way off? Any pointers appreciated. -- Don Henson