Without giving you a short course in electrics, the general idea is to test if 12v is present at the blower, or resistor pack. If it is then the switch is probably fine.

Turn your ignition on, and fan to speed3.
Turn your multimeter to measure 'Voltage DC' and hold the black probe on a bare metal chassis contact point (ground) whilst probing various bare metal legs of the resistor pack and blower power connector with the red probe whilst looking at the readout.

Be very careful not to short anything out with your probes.
If you don't understand what I've written, then I'm afraid it's time to call a friend in. Good luck.

>edit - earlier posts discuss replacing the switch, not something i have done.