How to measure TOTAL Amps?

current A= dq/dt. dq is the amount of charge and dt is the time period. Therefore, total charge Q = dq/dt*time. You can select the unit you want

It depends on many things. Fast charging and fast discharging both waste energy. Batteries have a self discharge rate that also wastes energy if they sit unused for any time. BTW, what maters is Watt-hours, the product of power and time = energy, not to be confused with Watts/hour or Amps or Amp-Hours.

https://www.solar-facts.com/batteries/battery-char...

https://batteryuniversity.com/learn/article/compar...

You can use an off-the-shelf watt-hour meter (e.g., "Kill-A-Watt") and calculate the amps from there.

Buy a lithium ion charger that has this facility. Quite a lot of them do.

You can then measure what goes in in mAh, and also discharge the cell and count what comes out.

1 amp-second is 1 coulomb of charge.  The total charge on the battery can be found by measuring the current in amps (every so often) with an ordinary ammeter, and integrating over time (as the current will likely decrease when the battery has more charge on it)

You are mixing units.

Amps is a measure of current. It is similar to the flow of water as Gallons per minute.

What you are asking for is the capacity in AMP HOURS (AH)

You can measure that by measuring the current in amps and timing it in hours, minutes or seconds.

The drawback is that the current will fall off as the battery charges up. You can take the beginning charge rate and the ending charge rate and averaging them.

(Begin+end)/2 or use a computer to measure the current every minute and average it over the period. Either way will be close, not NASA close but close enough for the sane community.

You might want to look at a charge that measures mA-hr input to the battery.  One example is here: https://www.amazon.com/Universal-Zanflare-C4-Recha...

I suspect there are similar meters to measure output mA-hr, but I leave that searching to you. 

You are totally wrong on measurement, ampere meter measures Ampere, not Ampere/Hour !

You need a data logger which you can probably build from an Aurduino, or something similar.

You need to sample the current over time. For battery charging, once per minute is good enough. For battery discharge, the sample period depends on what type of load the battery is connected to (current consumption relatively stable or varies). From that you can calculate amp-hours.

As Bill stated, people usually use watt-hours as a metric. If you add a voltage monitor to your setup, then you can calculate watt-hours by integrating the power measurements over the charge or discharge time span.

you want amp-hours, not a parameter normally measured. 

More useful is watt-hours, as watt is a measure of power, and watt-hour is a measure of energy. 

If you really want amp-hours , measure amps at various time intervals, say every 10 min, and from that calculate amp-hours.  1 amp for 2 hours is 2 amp-hours. 100 mA for 4 hours is 0.4 amp-hours.