The mAh rating should be written on the battery. For Lipo batteries typically used in drones, the stated mAh is usually a fairly decent estimate of the actual, though that varies some depending on the brand and quality of the battery supplier and the current load and age of the battery. Even if there is no label on the battery, the mAh rating is typically printed on the side of the cells. If there is no label printed with mAh capacity, or you don't trust the stated mAh, you can discharge the battery till the resting voltage is about 3.7 volts per cell under no draw, and then charge it back. Your charger should tell you how many mAh were put back into the pack, and you can typically multiply this by about 1.2 to get an estimate of the total mAh available in the pack. It's not 100% accurate, but it's a safe ball-park. Regardless, the number you get will be a good value to use when estimating functional capacity for flight time estimates.
You typically won't want to draw your battery much below about 3.3-3.5v per cell under load, and it should recover to around 3.7v resting with no load. You don't want to use much more than about 80-85% of the overall mAh capcity of the battery. A resting voltage of 3.7v should get you right there, but if you have way of measuring mAh consumption via a current sensor, it will be much more reliable than relying on voltage alone, as voltage can fluctuate dramatically depending on the current draw load on the battery and the quality of the cells.
Another thing to be aware of is as your battery ages, the useful capacity of the cells, as well as the safe current draw, can reduce somewhatfairly dramatically. You'll need to continually monitor the health of your packs throughout their life, and if you start to see a dramatic drop in performance, stop using them and replace them immediately.
Keep in mind this is true only for LiPo batteries we typically use. If you want to use Lithium Ion, the safe discharge voltage and discharge rates are very different, and the claimed mAh ratings can be dramatically off depending on the reliability of your source for the Li-Ion cells. Some 18650 style Li-Ion cells have been found to contain powder filler and a much smaller cell inside, so be aware of those caveats. Li-Ion cells are also typically safe to draw down to around 2.5v per cell rather than the 3.3ish of LiPos, but that as well as the max recomended current draw can vary depending on the manufacturer. If you have Li-Ion cells, be sure to check the manufacturer supplied specifications if you can find them, and make sure your cells are genuine. Knockoffs are a problem in the Li-Ion world. In general Li-Ion is only suited to applications that have both low current draw and low transient spikes, and there is much more variation in quality and specifications.
For both types of cells, keep in mind the current being drawn from the battery can dramatically impact the ability of the battery to deliver its full capacity. The higher the current draw the less usable capacity you will have regardless of the true pack capacity. This is why it's always the best idea to confirm both the current delivery performance, and the mAh rating if you have any doubts, and why running both a current sensor and voltage sensor in the air is ideal.
As far as identifying other characteristics of a battery, using a reliable "internal resistance" meter can tell you a lot about the battery performance and how much current you can safely draw from it. I use the Wayne Giles meter, and you can find a good discussion on the theory and how to use the meter here: https://www.rcgroups.com/forums/showthread.php?1323465-ESR-IR-Meter-fo-Lipos