I highly ercommend the GIMP. It really is just as good as Photoshop. Extremely powerful. Unless you want to do some print jobs (GIMP doesn't support CMYK colours), or unless you want to get a job in the industry (where Photoshop is a standard), you will never need another graphic editor once you master your skills in the GIMP.
There are not many freeware apps that are just as good as any commercial ones, but this is one of them. There are also some excellent tutorials to help you through. But the key here is time and practice. But then again, that's tru for any application, aven and especially Photoshop as well.