Mike Zamansky has Video #25 in his Using Emacs series up. This time it’s about how to use tramp. Strictly speaking, you could do what tramp does by using scp to bring the remote file to your local machine, edit it with Emacs, and then scp it back. No one’s going to do that of course, so tramp is really useful if you frequently have to edit files remotely.
As Zamansky explains, you can also use tramp to edit files on the local machine with sudo. You can even edit remote files with sudo using tramp but the method’s not obvious. Check out the video for the details. If you need to edit remote root files a lot, you may find the method I detail here useful.
If, like me, you’re an eshell user, you can simply cd to the remote machine from eshell. That method uses tramp under the covers. Here’s an animated GIF from Bodil that shows the process in action.