Unfortunately there is no easy way to accurately remove the unwanted background out of your image. But with a little practice this manual method can be achieved very quickly.
You can use this method on any image regardless of size or resolution.

Open your image in Photoshop and go to the "Layers" list (Window > Layers). Your image is probably on one layer, if not you can flatten your image down to one layer by clicking on the small arrow head in the top right hand corner of the layers list scroll down and click "Flatten Image"

With your image containing only one layer, select that layer and drag it down to the small page icon at the bottom of the layers list. This will duplicate the image onto a second layer. It is this second layer you will be removing the background from.
Select the original first layer again and drag it down to the small bin icon at the bottom of the layers list to delete it.

I recommend using the pen tool as it gives you the most flexibility. The more accurate your tracing the better your result. Continue tracing around the required portion of your image with the last point being on the very first point to close the path you have just created.
With the path closed open up the "Paths" list (Window > Paths) and click on the small arrow head in the top right hand corner of the paths list scroll down and click "Make Selection" ( Feather or anti-aliased selection is optional)

NB: If you are using Photoshop 5 or 5.5 you will also have to delete the path, to do this click on the small arrow head again scroll down and click "Delete Path". If you are using a later version of Photoshop the path will be removed automatically when you turn your path into a selection. With the selection do a copy and paste. (Edit > Copy > Edit > Paste)

This will put the area that was inside the selection on it's own layer.

  Now is a good time to save the image with a different name from the original. You can delete the original layer or keep it for future alterations, but you must remove it before you separate the image.

Another good tool for making a selection around the area of your image you want to keep is the magnetic wand tool which in Photoshop 6 and 7 is been greatly improved from earlier versions.
The Lasso tool is also good for making a more freestyle kind of selection.

Check out the tutorial "Better Backgrounds" for a more automated way of removing the background from your image. This tutorial is also a great way to quickly and easily transform a scanned image into a t-shirt design