The methods I'm familiar with involve essentially hooking either a resistor or a current sink to the battery and draining it until you hit a threshold voltage.
We used a Yokogawa recorder to record voltage during a discharge from fully charged battery to fully discharged. We sampled once/second and transferred the result to an Excel sheet where we calculated current and power (constant load resistor value). Summing the current and power columns gave us ampere-seconds and watt-seconds. We also got a nice voltage/time diagram.
You can use any hardware that produces Excel files as an output.
