mAh refers to the capacity of the battery. Your 3000mAh battery can theoretically deliver a current of 3000mA for one hour, 300mA for 10 hours or any combination where mA X Hours = mAh capacity. 1000mA = 1AMP.
I say theoretically because there is a limit to the amount of current a given battery can deliver. Some types are capable of pushing out more current than others.
It's kind of like a tank of water with a pipe coming out.
mAh is the size of the tank
mA is the size of the pipe
The bigger the pipe the faster you drain the tank.
To answer your question, the only way you can check the capacity of a battery is to drain it whilst measuring. Some smart chargers will do just that.
In normal use however the voltage (under load) is a reasonable indicator of how much capacity is left in a battery.
Hope this doesn't confuse
Terry