For rough operation in Wh, you can simply multiply Ah by the nominal voltage of the battery (as opposed to whatever its current voltage is), assuming one is working with a single voltage and a single battery.
For accurately measuring energy usage, you'd integrate the instantaneous product of voltage and current over time--which is basically what an electric meter does. Of course, with AC power, phase relationships and power factors must also be considered; but for a DC meter, there are no phase relationships to worry about.
To determine the state of charge of a battery, simply integrating net charge or net power is too naïve to be useful, since the response of a battery is hardly linear thanks to the Peukert effect, among other things. To figure that reasonably accurately requires more complex math. I suspect in the majority of cases, determining the state of charge is really the goal, rather than just how many amp-hours or watt-hours have gone into or out of the battery.