Each electron that travels through a circuit carries 1.602 x 10^-19 coulombs of charge. The circuit's current measures the flow of this charge, with billions upon billions of electrons adding up to a significant charge flow. The longer a current flows, the more charge it carries. You can calculate the current through a circuit, and the result charge that passes through it, from the circuit's voltage and resistance.
Add together the resistances of the circuit's resistors. If it has, for instance, two resistors of 3 ohms and 5 ohms each: 3 + 5 = 8 ohms.
Divide the voltage across the circuit by this total resistance. With a voltage, for instance, of 12 volts: 12 / 8 = 1.5. This is the current through the circuit, measured in amperes.
Multiply the current by the length of time for which it runs. If the current runs, for instance, for 10 seconds: 1.5 x 10 = 15. This is the number of coulombs of charge that pass through the circuit.