This is a quick and dirty (ahem, well, not that kind of dirty) guide to making 5- and 7 volt connections for your fans. You'll fanclub will probably remain pretty small if you electrocute the members, though. Tough.
Your standard computer fan runs on 12 volts. However, most (practically all) of them can also run an lower voltages, which makes them a great deal quieter. Of course, when slowed down, they also move less air, possibly causing problems with overheating. As such, do this at your own risk only.
To create a 5 volt connection you'll just need to plug the positive lead of the fan to a 5 volt lead, provided standard by the computer's power supply. However, often a better compromise between volume of sound and volume of air moved can be accomplished by using the 7 volt connection. This is accomplished by using 12 volts for the positive lead as normal, but at the same time giving 5 volts on the negative lead (12 - 5 = 7).
Theoretically there are some slight risks involved in making the 7v connection this way. For example, it could short circuit the power supply if the fan breaks. Under normal conditions, it works just fine for many people. The 5v connection does not have these risks if done normally, just make sure your fan will start every time at such a low voltage (some 120mm fans in particular won't).
To make 5 or 7 volt connections, you'll most likely be wanting to plug the fan into a connector coming from the power supply (see figure 1).
If your fan already has a suitable connector (see figure 2) to plug into the power supply, you'll just need to rearrange the pins on the connector coming from the fan.
The pins have small "hooks" to hold them in place (see figure 3). The connector, the hooks are bent out (marked 1) so they won't fit through the hole in the connector. To detach the pins (in an unviolent manner), you'll need to push the hooks back in (marked 2).
To accomplish this, use a screwdriver and circle its head around the very base of the pin inside the connector, pressing against the pin (see figure 4). After this, pull the wire from the back of the connector. If you succeeded, the pin will come out gently. If not, the hooks are still too far out. Repeat with the screwdriver.
To re-attach the pin, simply "open" the hooks again and push the pin back into the connector. Tug gently at the wire to verify that it will stay put.
For the 5v connection, move the pins from the 12v (yellow) connector and its adjacent ground (black) connector to the other two connectors (5v and its ground). For the 7v connection, leave the 12v connector as it is, and move the adjacent ground connector to the 5v (red) connector. The fan only needs two connectors, the extra two need not be attached (if they even were there in the first place).
Warning: If you use fan adapters which also provide a female connector to chain in another device, make sure you don't use that connector for anything except fans after this. Plugging a hard drive there would not be wise with the "wrong" voltages now present there... Then again, chaining multiple fans together like this works just fine, as you only need to modify the first.
Unfortunately many fans ship with motherboard connectors installed (see figure 5). These have only the 12v lead, ground and possibly a third lead for RPM monitoring information. Note that different manufacturers use different colors for the wires, so be sure to double check the order (see figure 5).
Since the motherboard only gives 12 volts for such a connector, you'll need to either cut the fan's leads or detach the pins from the connector, and plug them to a connector coming from the power supply. Of course, you could also buy an adapter and then follow the instructions above for connecting to the power supply...
Like their siblings in the power supply, the pins inside the motherboard connector also have "hooks". In figure 6, the "open" hook is marked 1 and the "closed" hook is marked 2.
To detach the pins, you just need to press down on the hook and simultaneosly pull on the wire to get the pin out (see figure 7).
A good alternative to detaching the pins is just cutting the leads and stripping the ends, since the pins cannot be rearranged in the connector to provide different voltages (well, except 0v).
Once you have the wires free (cut or detached, whichever), you can shove them. Into the power supply connector. With the pins still attached, it is possible, but may require flattening them , since they are too large as such to insert into the holes. Withouth the pins, I recommend you strip maybe 2cm of the wire and fold it in two or three to make the end thicker so that it will feel better inside.
Once inside the connector, fold the rest of the wire against the connector and apply duct tape liberally to secure it in place.