I was going to write up a long dissertation on using a Voltmeter, Ohmmeter, or Ammeter, (and how not to damage your meter) but there are sites on the web that outline it "fairly" well:
http://www.saskschools.ca/curr_conte.../lesson12.html
and
http://www.tpub.com/neets/book16/69.htm
In general, though, you can damage a meter if you leave it in the wrong function, (like set up for measuring milliamps), and then go to measure something else (like voltage).
VOM Analog meters (the ones with mechanical needles--D'Arsenval movements), are the easiest to damage. Least likely to damage this meter would be when using it to measure VOLTAGE. And if you're not sure how much voltage you're gonna be measuring, generally start on the highest scale, and click your way down untill the meter reads 1/3 or up near full scale. VOM's can be damaged by rough handling (damage to the movement).
Leaving it on OHMS (resistance measuring), and then placing voltage on the meter could damage the meter. Definitely in the Ammeter mode and going to probe for voltage will damage the shunt and/or movement, or it may blow it's internal fuse....
DMM (Digital Multi Meters) are a lot more forgiving if you happen to leave it on Ohms, and probe for voltage. But same applies in Ammeter mode...it will pop it's fuse if you go to probe for voltage. DMMs can take a bit of rough handling (no sensitive moving parts).
Rule of thumb: ALWAYS CHECK THE MODE THE METER IS IN BEFORE TAKING A MEASUREMENT or even inserting it in a circuit.
And try to remember to turn the meter to OFF when you're done.
That said, I purchased several DMM's at Harbor Freight, because these things are throw-aways if you damage them. They go on sale for $1.99 (and that includes the 9V battery!!!)
These POC (pieces of Crap) even have a 10A DC scale built in. I thought I smoked one of these recently, but it turned out to be the crappy test leads (burnt open)...( I knew the value I was going after was going to be about 4A, but was not aware of the inrush, momentary surge current of about 18A !)
Another word of caution is to avoid directly measuring higher voltages...at work, our MIL Standard guidelines are "under 300V" for hand held probes. Over 300V, we have to make sure the measurement points are done via a voltage divider array of resistors.