The computer you want to run the application on is the one you run ssh -X from. I recommend ssh -fXTC hostname_or_ip application_name. -f forks to background, -X is for X Forwarding (must be enabled in sshd_config on server), -T is so it doesn't assign a tty, and -C is for compression.

If you are sitting behind your computer and want to run an application running on the NIT and let it show on your computer you first SSH to your NIT. Then you run the ssh -X hostname_or_ip (again, I suggest earlier mentioned command instead) with the hostname_or_ip being the one of the computer you're sitting behind. Now, your NIT application will be shown on your computer (including copy/paste and all that ). Because the program runs on the NIT it won't be any faster, and because you're using encryption, compression, and WiFi you'll have a bit latency.