This is a very quick video I made to demonstrate using the lasso tool in Photoshop (so it will look different if you are using Photoshop Elements).

I've used a very small window for the video, if I was doing an image like this for real I would make the window full screen and zoom in a lot, as well as taking more care that the lasso selections followed the outline of the photo subject much more exactly. The nice thing about doing it this way is that you can make as many selections as you want and add to them or deselect parts, before deleting using the 'delete' key on your keyboard to delete the background around your subject. (Notice that when you are in 'add to selection' mode there is a + symbol next to the cursor. Deselect puts a - symbol next to the cursor.)

After you've completed your project remember to save your background image with a new file name to avoid overwriting your background photo. You can close your subject image without saving, or keep it as a photoshop file (not a jpeg) so that you have a ready cut-out subject for putting into different settings!

To share over the web, choose the 'Save for the Web' option under the file menu.