There's two ways to do it. I suppose the easiest and fastest way is to just use the eraser and erase the background.
1. You'll have two layers, the white background layer and your picture you want to remove the background from.
2. Have your picture above the white background.
3. Make sure your picture you're removing the background from is selected in the Layers section.
4. Erase the background.
a. Use a big solid round brush for large areas.
b. Use a smaller fuzzy round brush for close to the dinosaur (or whatever you're cutting out).
5. Once the background is all removed, you can delete the layer called "background" so that you only have one layer, the dinosaur.
A way to do it better (it will look better, but takes FOREVER) is by using the Paths tool. Here's the video I watched when I did
THIS:
http://www.youtube.com/v/vb8zg4B1wt8&hl=en_US&fs=1&rel=0Have fun!
Oh, coincidentally, that's the render I used when I made your red sig with the Alien, haha -
http://www.bfmracing.net/forums/index.php/topic,45027.msg339386.html#msg339386