To calculate the internal resistance in a circuit, first determine the voltage drop across known resistors, such as a 5-ohm resistor, to find the current. The internal resistance can be represented as a resistor in series with the battery, affecting the overall voltage measured. By labeling the internal resistance and the measurement points, one can derive equations that account for the voltage drop across the internal resistance. The discussion emphasizes the importance of visualizing the circuit and writing out the relevant equations to solve for the internal resistance. Understanding these concepts is crucial for accurately calculating internal resistance in electrical circuits.