I'm sure a Gimp user will be along eventually to show you where the image size controls are.

Again, if you're not printing, dpi is irrelevant. You can set your dpi to 20 or 20000, and it won't make a bit of difference to how it appears on the screen or the file size. Further, it can be changed after the fact if you decide you do want to print. If, for instance, you decided you wanted to print your 1024 x 768 image to an 8 x 10 format (8.5 x 11", minus reasonable margins), you can just do a little bit of math to get it to come out to the right size. The long dimension is 10" and 1024 pixels, so that makes it 102 pixels (dots) per inch. The short dimension is 768px / 8" = 96 dpi. So somewhere in the range of 100 dpi would make your 1024 x 768 image letter-sized.

If you need a 24" x 36" image at 150 dpi (a decent poster print, but nothing you'd hang in a gallery): 24 X 150 = 3600px by 36 X 150 = 5400px.

It should also be mentioned that the paper makes as much difference as the print density.