If you just want to use emacs, simplest thing is to start it in a console with 'emacs -nw'. This stops it trying to open a window in the local machine, and it runs in the console instead. Since emacs was originally designed to run this way, there is not much loss of functionality.
Otherwise I think you do something called 'X11 forwarding'. See the tutorial at
http://www.aperiodic.net/phil/ssh/
for example, or search google for '"X11 forwarding" ssh linux' for lots more info.