To check AC current using a digital multimeter, it's crucial to understand that standard multimeters are not safe for measuring household line voltages, which can be lethal. A clamp-on meter is recommended for such measurements. In a specific case involving a 5.4Vac indicator lamp, the user is attempting to determine the current draw to find a suitable replacement bulb. However, without knowing the current, it's difficult to ensure the replacement bulb will function correctly. Suggestions include using a DC supply or batteries with resistors to approximate the necessary measurements.