First of all if you're not familiar with the internals of a computer don't even think about this, it's way too easy for a newbie to blow up a fan this way. :)

The first thing you should try is called the Fan Poke Method. This is not at all what it sounds like its way too easy for someone to stop the fan and blow it up. Granted the name is a little deceiving but this is one of the best short term and sometimes permanent fixes.

Step 1

Take a normal piece of paper and rip off a small strip fold it up a couple times to give it some strength, not too many folds because it still has to be somewhat thin.

Step 2

Slide the paper in between the spinning part of the fan and the base being careful not to stop the fan's motion. Repeat until the fan is no longer grinding or until it's spinning fast enough to properly cool the power supply.

The next way and probably best way is to simply replace the defective fan. However, this is for advanced users only and will more than likely void any warranty you may have.

Just steal a properly operating fan of the same type, voltage and size, from an old case or old crappy computer. Then turn your computer off, unhook the power supply from the mainboard, hard disks etc... and remove it from the case. Pop the cover off the power supply and remove the defective fan, you may have to cut the wires connecting the fan to the power supply if its one of the cheaper soldered on deals. Cut the wire at a a sane length so as to make it easier to attach the new fan easier. DO NOT RIP THE WIRE STRAIGHT OF THE PC BOARD. If you do this and you don't know what you're doing you can easily fry the power supply and/or your computer. :) But that's easily avoided by leaving a good length of wire. Now simply fasten the new fan in place. Make sure it spins the same direction as the old fan. Now attach the wires from the new fan to the ones the old fan used. You can solder the wires together if you wish or simply twist them together well and tape the crap out of them with electrical tape.

There ya go, I have done this many times, especially the poking the fan with paper part in many situations. Replacing the fan is almost always inevitable in the long run but the poking with paper can be fun. :)

This method could be applied to any fan really just be careful as fans in computers are very delicate and if they break your computer could easily overheat and burst into flames. :)

Yes yes, the word of warning on the capacitor thing is indeed wise, DO NOT TOUCH ANYTHING BUT THE FAN AND ITS 2 WIRES. There are no capacitors with high enough voltage to kill you in most power supplies. However, there may be so BE CAREFUL and make sure an adult helps you ;)