I'm presuming that you mean the background in an image, not the picture on the desktop, right?
There are masses of ways to do this - some of which, depending on what version of Photoshop you have, may or may not be possible. Some techniques are also better on certain situations than others.
If the background is predominantly in a single colour (a clear blue sky, for example), the Magic Wand tool is what you need. Just click on the background you want rid of, it will select everything of that colour - all you need to do is hit delete. You can adjust the tolerance of this tool to suit your needs: the higher it is, the larger the range of colours are selected.
There's also the quickmask tool hidden away. It's a little more complicated, but it's a lifesaver at times. Once this is selected, you just paint the areas you want selected in black (it'll actually come up a transparent green or red) and then switch the quickmask off again. Anything you painted in black is selected and you just need to hit delete to get rid of it. Just paint in white to get rid of any areas you didn't mean to select.
There's also a range of selection tools, although getting accurate results this way is really quite hard. Remember to save the original file and do the editing on a copy.
If you need more info, have a look in the manual - you're looking for the stuff on selections.
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Edit: Sorry for the long post, but there's a little more...
I notice you need to add a background. To do this, you need to use anotheer lifesaving feature in Photoshop (and nearly all image editors) - layers.
After you've selected the background you don't want and deleted it, you need to go into the Select Menu and go to "Invert Selection". You'll then need to go into the Layers menu and find an option called (something like) "Promote to Layer".
This gives you two layers: the background and you're selection. After that, you need to go back into the layers menu and select "New Layer". You need to then put this layer below the layer you made earlier, and then paste in your backgroud pic.
Phew, eh?
