After you take it off the charger, let it rest a few minutes, then set the meter to DC and volts, and put a + probe on the + end of the cell, and the - probe on the - end of the cell, and read the volts.
If your light only uses one cell, you don't have to worry about matching cells, etc...because with one, you won't have a potential difference between cells, etc. (Heat build-ups/Fire risks, etc...)
You typically want the cell to read 4.2 v +/- 0.05 v (4.15-4.25 v) depending on the cell's specs...but a hair lower is better in the long run, as the cells tend to last longer with "all but" full charge vs FULL charges...so 4.15-4.17 v, etc, is a common desired target.
If its a protected cell, and a decent charger, etc...you will most likely be fine. The main reason you're bothering to check the voltage after charging is to qa/qc the charger...to make sure its not overcharging the cells, etc.
After you're done with the cell, and ready to put it back on the charger...you check the voltage before you put it back on, so you know how low you got it down to (Cells have minimum charge requirements too, and you don't want to drain them down lower than that limit, to help prolong their lives, etc.)
Once you're used to it, its a few seconds here and there...not a big deal.
If only for this purpose, most people seem to be fine with almost any volt meter device, but digital multimeters seem to be preferred. I use a Fluke 115, because I have it for work, but lots here use inexpensive harbor freight versions, etc.
I have lights that take up to 6 cells at a time, so I'd rather have a DMM I feel confident with, but if sticking with single celled lights, while a better DMM is of course better, you would probably be fine with anything that read out what you needed.
Cottonpicker (CPFM) for example has a simple voltmeter for this purpose, etc.
:D