What not to do with a Multimeter
One thing very typical among amateurs is to try to measure current by connecting the amperemeter (or multimeter set to "measure current") in parallel to the circuit where the current is to be measured. See this question for an idea of how that happens.

The extreme of that looks like this (one shouldn't even consider repeating this). A person with a PhD in physics grabs a multimeter, switches it to "measure current" and thinks "Oh, let's measure the current in the mains outlet". Then he inserts the probes into the outlet which shorts the outlet and causes circuit breakers to trip. The meter survived btw and I have no idea why the fuse didn't blow.

What happens here? An amperemeter has very low resistance, so connecting it in parallel to the circuit in which a current is to be measured shorts that circuit and also the circuit powering that circuit (since they are connected to each other). This may result in very high currents and lead to the meter fuse blowing or even worse consequences.