how do I start a gui application and the Desktop on a remote computer threw ssh

I have an ssh question that I have not been able to figure out.

I am sitting in front of computer A on computer B I would like to start mplayer and have it display a movie on computer B's screen. I think a better question might be how do I start a gui application and the Desktop on a remote computer threw ssh.

Thanks

[Partial SOLUTION]

Problem 1

To start say mplayer on the remote machine do the following.

Local Machine
Log into the remote machine.
ssh me@192.2.2.2

Remote Machine
export DISPLAY=:0

mplayer ILoveLindyLex.avi

Now mplayer will play on the remote machine.

Problem 2.

How to start the remote Desktop?

Thanks, Lindylex

You are better off not starting a remote desktop, but run one on your local X server. Start a terminal window, and connect to the remote system with SSH using the -X argument (upper-case X). That enables X11 protocol forwarding to your system. Once you are logged into the remote system, your DISPLAY environment variable should resolve to your local server, so when you start X applications on the remote system, their output will tunnel thru the SSH connection and show up on your local display. I have done this frequently in the past.

That said, running videos over a WAN generally don't work too well. They use a LOT of bandwidth, so if you don't have at least 10mbps between the remote system and your local system you probably won't be particularly happy with the results. Also, there is all the encryption of the data stream going on, and that is going to place a big load on both sides of the link, but the biggest on the remote host side as encryption is generally more CPU intensive than decryption.

So, in my experience, there is no good way to play videos remotely this way. You would be better off running a video player on your local system, and only have the data passed over the wire, but that means you need to pipe the video data from the remote system to your local player. Since video data is already compressed, it isn't as big an issue, and a 5-10mpbs link will handle (in theory) a 720p high-def feed.