How exactly does a current meter circuit work? Does it use a form of voltage over a miniscule ohm resistor measurement to calculate the current? Or some form of hall sensor? I just don't see how the voltage drop measurement wouldn't be highly inefficient and how the hall sensor could be accurate. Is there a better way?
The voltage drop across a current viewing resistor is referred to as "voltage burden."
A resistor and a volt meter form the simplest and often the most accurate DC current measurement circuit. As with every design there are tradeoffs. Some of the tradeoffs for DC current measurement are accuracy, temperature coefficient, floating or ground referenced, power dissipation, voltage burden, short circuit survival, size, and cost.