Death From Above wrote:
I have a mongoose mountain bike with 3 gears in the front and 7 in the
back. The rear derailleur is all bent up and needs to be replaced.

Is it easy to do? Do I need special tools? What kind of rear
derailleur should I buy? Are they any good cheap ones online?

It's easy once you get the idea. You need Allen wrenches (usually 5mm and
3mm) and a small screwdriver. It's good to replace the inner cable at the
same time, so you'll want decent cable cutters too. If you don't want to
break the chain, the rear plate of the cage needs to be removed via the
jockey wheel bolts. You'll find full instructions online for fitting and
adjustment.

Probably any Shimano long cage derailleur will be fine. Look for one
described as 8 or 9-speed. This will also work with 7-speed.

~PB