Pick yer poison
There's 4 mainstream ways to do it.
1) Telnet. This gives you a console on the machine you are connecting to, but isn't encrypted and hence is insecure.
2) SSH. Basically an encrypted form of telnet. Both SSH and Telnet are plenty to admin a machine remotely. If you want/need a GUI, you can use...
3) VNC. You just need to install the VNC server on the computer you want to control, then use the VNC client software to control it. Works basically like PC Anywhere. You _CAN_ use it through a web browser like penguinfreak said, but you don't need too.
4) X Window System Network transparency. You can have an X app execute on another machine, but have all its interactive stuff (window, buttons, etc) appear on your stream. This is only going to be useful for remote administration if you have a handful of admin-type apps that are X-based. Note: you don't get the full remote desktop this way, you have to launch X applications on the remote computer in such a way that they display on your machine.