The reason your A/mA (amperage) reading was fluctuating is because when a multimeter is set in A/mA mode, its internal resistance is almost zero. So when you attach it to the Arduino's power supply, it shorts it, and the Arduino struggles to supply enough power. This causes it to fluctuate.
As for learning about the basics of electronics, here are some good books to look at:
Getting Started in Electronics by Forest Mims, III
Make: Electronics by Makemagezine