Hi,
To measure the current into or out of a battery you can use a current meter, or a resistor in series with the battery and measure the voltage across the resistor and then use Ohm's Law to calculate the current. For example, using a 1 ohm resistor (of the correct wattage) if you see a 0.1 volt drop then you have a 0.1 amp current. But usually we use a smaller resistor like 0.1, but then again it depends on the current and how much voltage drop is acceptable.
One catch is when the battery current is very very high like 100 amps or 200 amps. Then we have to be more careful what we use to measure that current. Most likely a current shunt or a clamp on DC ammeter. Clamp on DC ammeters measure current without having to break the circuit and are accurate enough for most battery applications. However, some clamp on ammeters are sold as DC ammeters when really all they measure is AC current, and they can say "DC" because they also measure DC voltage. So if you want to purchase a Clamp On DC Ammeter then you need to make sure the spec's state that it will measure DC current. Most of them also measure AC current too.