Ok go DC Voltage (its the two lines that go straight, think one is dotted) if you dont have an auto ranging multimeter make sure it will read Volts not mV or anything like that
Put negative probe on a good chassis earth and put the positive probe into the plug with the fog light switch on.One of the terminals should have about 12V (there a 3 pin plug, should be a power for indicators, power for foglights and common earth)
So if theres power at the plug, check the earth is ok. Change the multimeter to risistance (the omega symbol) and keep the negative probe on the chassis earth and probe the terminals with the positive. You should have one of them with a low resistance (OL is outer limits and means there is no circuit, you dont want this, you want 0.0ohms or similar, it will probably show more like 6ohms or so)
If you have power and earth (I'd assume you have a good earth if your indicators still work) then there is a problem with the actually light, wether it needs a new bulb or the wiring in the light assy is a bit dodgy
If there is no power there, then post up here