A battery is considered to be an EMF in series with a resistor.
You can measure the EMF by measuring the open circuit voltage of the battery. There is no voltage drop across a resistor if there is no current flowing through it.
To put a load on the battery and measure the current and voltage, you could use something like the attached diagram.
A voltmeter monitors the output voltage. A variable resistor R is placed in series with the ammeter.
You can monitor the voltage while the heavy load (R) is placed across the battery. A large rheostat would be suitable for R.
Suppose R makes the output voltage drop to half. Then you could say that R is equal to the internal resistance.
You can calculate the value of R by measuring the voltage across it and the current through it.
The voltage does not have to drop to half. If you were testing a rechargeable cell, a NiMH or NiCd cell, you would not do this because these can deliver very large currents. So, maybe a 10% drop would be OK for these.
You just calculate the value of the internal resistance knowing the current flowing and the voltage drop between no load and the measured load.