using the multimeter

Clarifications

But if you mean FAN, then 12vdc

20 Volts DC

You also need Wattage or Amperage as you can have Voltage without and Current and still not have the Fan working. So you need to test the Voltage and Current if you have a Multimeter that has the Current Option.

Using the Multimeter set to 20 V DC for any computer work is sufficient for all Voltage Testing.

Col

You need to use the 20 volt DC range, and measure the voltage with and without the fan plugged in. Also measure the AC too, this will give you an idea of how well the power supply is filtering the DC voltage. The AC reading should be less than 100 millivolts AC, if it's more, replace the power supply.

I know that we suggest using a DMM often. It is a very good trouble-shooting tool.

That said, unless you know what you are doing with the meter, it can be difficult to understand the data.

Major meter manufactures like Agilent, Fluke and Keithley all have usage guides that you can download and review.

Good motherboard manuals or web sites like Hardware Book
http://www.hardwarebook.info/
Provide information on connector pin-outs and expected voltages.

Now, the standard probes that come with most meters are useless for all but the most basic of tasks.

I use either micro-grabbers or fine point probes most of the time.

The most important thing is to make a good connection without shorting the probes to nearby connections.

Most CPU fans have 3 lines. Power (usually 5 volts) Ground (return) and Tach.
The tach output is a pulse directly proportional to the fan speed. Most cheap DMMs cannot read this signal properly.

In all the systems I've worked on, I have only seen the fan power connector fail once.

If your CPU fan does not spin, or spins slow, the first thing to check is does the fan itself spin freely when power is off.
If the fan blade does not spin free, then the bearings are shot and you need a new fan.

Chas