Will this work? Does it fit? I know my psu shouldn't be a problem since the gtx260 consumes more power. Or am I wrong here?
Can I just replace it myself? I figure this shouldn't be too hard?
A straight up swap should be no problem. The 260 is a 180w card and the 660ti is 150, so if the 260 causes no power problems, the 660ti should be fine. As far as doing it yourself, absolutely. Make sure you have the latest drivers installed, shut down your computer, unplug from wall, wait a couple minutes for the caps to discharge (or press power on button), remove 260, install 660, plug into wall, turn on and go.
As a note, be careful at the rear of the card slot - the locking tab must be pressed down to remove the old card. When you install the new card, the tab should make an audible click when it locks in the card (like when installing memory).
Make sure you are grounded (touch the case) before and when removing/installing cards - static is NOT your friend.