I'm not an expert in batteries, but equipment needed would be an ordinary dc voltmeter to monitor battery charge, and some kind of amperage meter or current totalizer to measure currentXtime (= amount of charge removed) as current is discharged from the battery. Best to start with a new or otherwise totally recharged battery. If you have something that can withdraw a steady current load (choose current outflow rate that is much smaller than maximum battery current delivery rating) from the battery (e.g. steady 0.10 amp drainage or 0.010 amp drainage); just note the drainage rate and the total time period over which the drainage occurred (all while monitoring voltage periodically or semi-continuously across the battery terminals). Amount of battery charge that is discharged = current (amp) x time. As the battery becomes depleted, the voltage across the terminals will decline, as will the maximum deliverable amperage--may need to step-down current drainage rate as terminal voltage becomes significantly reduced.
If battery is rechargeable, can repeat this measuring process as battery is being recharged (be careful to find a recharger that is suitable for that battery; can be safety hazard if recharge rate is too high!). However if recharger is delivering at constant voltage; will need to disconnect recharger from battery periodically and measure voltage across battery terminals (and then re-connect charging device).
Experimentally determining the open-circuit voltage (OCV) of a battery as a function of state of charge (SOC) commonly employs two primary methods. The first involves segmented discharging: starting from 100% SOC, the battery is discharged at a specified current (e.g., 0.5 C), with periodic rests at every 10% SOC interval to measure OCV once polarization dissipates. The second method uses low-current discharge (e.g., 1/20 C or 1/30 C), minimizing polarization effects to enable direct OCV measurement during discharge, as lower currents reduce dynamic voltage fluctuations and better approximate thermodynamic equilibrium. Both approaches facilitate the establishment of an accurate OCV-SOC relationship essential for battery modeling and management.