X actually has two completely different clipboards. There's the highlighting one and the copy one.
To use the first, just highlight some text. To paste it, click the middle button on your mouse. I use this one whenever I have my hand on the mouse (which is rarely).
The second is a conventional clipboard that's used the same way the windows clipboard is. Ctrl+C, Ctrl+V, etc. This one's great if you don't want to take your fingers off the keyboard.
Of course, you've also got the individual clipboard implementations in non-X applications, but you probably aren't interested in those