There are various ways to go about removing an image's background, and it just depends on the pic you're working on which method is best. As this thread develops tutorials various techniques and methods to remove an image from a background will be added.
A Simple Technique
By Spawn of Cthulhu. Use this Tutorial describing the following steps in detail using images and screenshots to extract an image from its background:
1. Open an image, rename the background as layer One.
2. Open the extract tool: Image>Extract or Option/Alt+Cmd/Ctrl+X
3. Trace around the image with the marker tool and use the bucket to fill the area to be kept. Click ok.
4. In the history pallette, click next to the image before the extract state.
5. Use the Eraser and Art History Brush tools to clean up the image.
6. Save the extracted image.
I use this method when pics have alot of the background blended with what you want to keep, like if Kirk is headbanging and his hair is sticking out everywhere. I also sometimes find it easier to just make my eraser 3 pixels wide and delete the edges around the part of the pic I want to keep, zooming in several times so I can see what I'm doing; I usually use this method when the pic is pretty much a good outline, i.e. Kirk's hair isn't flying out everywhere, lol. You should mess around with these ideas and play with them, there are still other ways to make a pic stand out from its background or cover up its background without actually removing anything, and sometimes it creates awesome effects, like my 15 Jun 03 Nijmegen, Netherlands cover, all I did was paste the St. Anger fist over the pic, lower the opacity, change the blend mode, and zoom in with a 3 pixel brush to delete the part of the pic covering James, and it turned out perfect.