If you have a multimeter it can measure current. But, your meter has to measure-down to a few mA and it will only measure AC or DC... It won't accurately measure the current of a pulse. For that you need a resistor and an oscilloscope.
As Wawa says, we rarely measure current. It's a pain because you have to break the circuit to insert the meter (or resistor). Most of the time there's a resistor so we can measure the voltage & calculate. Or, the voltage & resistance are known so there's no reason to measure anything unless there's a defect.
I work in electronics and I measure voltage every day. I might measure resistance a few times a week. ....Less than once a year I switch the meter to "current". (My bench power supply does display current (as well as voltage) so I can monitor the current of the entire board/unit, and I do keep an eye on that.)