Battery level - how to check
Two things happens to batteries as they discharge. The open-circuit (unloaded) voltage goes down, but there is also internal resistance in the battery that goes up with increasing states of discharge.

Depending on the battery technology, the voltage may gradually slope off over time, or it may only dip a couple of tenths before suddenly giving out all at once. So generally you can tell the difference between a fully charged battery and a nearly dead one by measuring voltage, but it can be difficult to tell with partially discharged batteries.

The internal resistance is what really matters anyway. You can't measure it by sticking an ohm-meter on a battery, but you can infer it by measuring the battery voltage while it's under a load. You need a load appropriate for the battery voltage and current capability, so you might use an automotive incandescent bulb for a small 12V lead-acid battery, or an LED for a coin cell. Just something you'd typically expect the battery to be able to power. If you measure the voltage while the battery is powering the load, you get a much better indication of how charged it is.