Gimp/Gimpshop

Gimp is a GPL licensed image editing application with a wide range of filters and features. You'll often find gimp plugins made available online implementing recent research papers before they make their way into the app. So it's a nice choice for getting to play with some cutting edge tools.

Another plus is you can use photoshop plug-ins in gimp.

Your package manager is likely to have gimp in it, so follow your distros standard instructions for installing applications using its package manager.

There is also an two applications available called GimpShop and Gimphoto, which takes Gimp and makes the UI similar to photoshops. If you combine GimpShop with custom keyboard shortcuts you may find it a good option if you're already familiar with photoshop. Gimphoto already has similar keyboard configuration and has the advantage of using a later version of gimp than GimpShop.