Using SSH to open application on desktop

This works for me once I'm ssh'd in:

export DISPLAY=:0; nohup <command> &>/dev/null &

For example:

export DISPLAY=:0; nohup iceweasel &>/dev/null &

When you're ssh'd in normally, set the DISPLAY variable with export DISPLAY=0:0 (0:0 being the display of the target box), and then you can run your command as you normally would. If you want to be able to close the ssh session, prepend the command with nohup: nohup ./yourcommand > dev/null.