Generally, both sides of the fan will have a set of holes so you should be able to re-attach the fan with the same screws. Reassemble and install the power supply. You should see a drop of several degrees inside the case just from this simple, free procedure. Opening the power supply will probably void the warranty on it so, if you're worried about that sort of thing, you'll be relieved to know that there are other things you can do to lower your case temperature. Adding a second fan is a good idea even if you aren't overclocking.
Many cases provide a location at the lower front that is designed for a second fan.
Even if your case doesn't have a ready-made mounting point, you should be able to find a spot to install a second fan. Depending on the type of connector your fan has, you can plug it into the motherboard fan connector or use one of the extra drive power cables for it's 12 volt supply. Leaving the case cover off is also a possible solution to overheating. Though not ascetically pleasing, it is a free solution that many overclockers employ. If your system crashes or seems to become unstable after a few minutes of operation, you may find that heat build-up is the problem.