Measuring electrical current is more invasive that measuring voltage.
Imagine water flowing in a pipe. To measure the flow, you would have to
cut the pipe and insert some kind of measuring device. Measuring
electric current is no different. You have to break the circuit and
insert the current meter into the circuit.
Measuring current. The meter becomes part of the circuit.
There are non-invasive current meters, called a current clamp or clamp
meter that can measure the magnetic field around a current-carrying
wire.
A multimeter with a current clamp
Simply clamp the meter around the wire. If the current is very low the
meter may not be able to give you a meaningful reading. In that case,
loop the wire and stick the meter through the loop. This will double
the magnetic field and double the current reading (don't forget to
divide your reading by two).
If there is a resistor in the circuit through which the current you
want to measure happens to be flowing, you can measure the voltage
difference across that resistor and use Ohm’s Law (explained below) to
calculate the current.