I reckon the following are the first two mistakes most of us make when using a multimeter:
1) taking a resistance measurement, then trying to take a voltage measurement without changing the dial back to the voltage setting - you can't measure the resistance of a live circuit and can damage the meter.
2) taking a current reading, then trying to take a voltage reading without remember to switch the positive test lead to the correct socket. This shorts out what you're trying to measure through the meter, blowing the tips off the test probes and either blowing a fuse in the meter, or damaging it if it's unfused.