Normally a multimeter will have three or four jacks on it. One is for measuring voltage (red), one or two are for measuring current (red), and one is for your ground (black). The ground jack is typically called common. To measure voltage attach your probes to the voltage measurement jack and common. In the picture they would be the two right jacks. To measure current attach your probes to the current measurement jack and common. In the picture the current measurement terminals are the two on the left. One is for measuring larger currents, the other for smaller currents.
Reversing the leads in either setup will not cause any problems, except your measurement will have a sign opposite the one you expected (1 would be -1). In the voltage measurement configuration you typically cannot break anything unless the voltage is too high for the multimeter. If you use the current measurement terminals when you intended to measure voltage you will probably blow the fuse in your multimeter, and possible damage what you were testing.