Simple current measurement solution and testing its validity
Well the best beginner starting place is to use the shunt resistor and setup it up so you can use an A/D converter to make voltage readings of the drop across the shunt resistor. The simplest starting place is to have the shunt resistor connected to GND on one side instead of working with high side current measurement. 

To get some correlation of readings you could easily use a digital volt meter to measure the voltage across the shunt resistor and also have it read what the A/D converter sees at its input.

The problem you can run into when trying to compare current measurements made by a digital multi-meter in current mode is that the meter itself has a shunt in side and this can change the amount of current flow in the actual circuit off enough to cause loss of correlation. Using the meter in voltage mode puts it in a fairly high impedance input mode thus keeping the meter from having as much influence on the circuit under test.