Lithium ion batteries (LiIons) are different from other rechargeable batteries:
1. LiIons hate being dead: Running the battery all the way down is very hard on it. And the worst thing you can do is to run it to exhaustion and then leave it sitting uncharged in the camera or bag for months. If the voltage of one of the battery's cells drops below a critical threshold, permanent damage can occur.
2. LiIons like being recharged: If you really wanted to maximize the life of your battery, recharge it after each use rather than waiting for the camera to show a decline in battery level.
3. LiIons like cool temperatures: Heat is the enemy of LiIons. If you have multiple batteries, it's best to charge them and then store them in the refrigerator (not the freezer). Just remember to take them out of the fridge a few hours before use so they can return to room temperature.
4. LiIons should stay svelte: If your battery shows signs of swelling, it may be time to replace it.
5. Watch out for cranky LiIons: If you are using an older battery and your camera glitches (fails to take a shot, stutters, locks up, does not save the image) or the battery level indicator fluctuates wildly, it may be time to replace the battery. But before doing that, cleaning the battery contacts with a pencil eraser might fix things.
The topic of chargers is a tricky one. A high-quality fast charger might be fine but a low-quality one might be bad. One subtle issue with LiIons is that the final charge voltage determines the total number of shots per charge and also the total lifetime of charge-discharge cycles. Charging to a higher voltage (4.3 V/cell) means getting about 15% more shots per charge (good!) but it also means losing up to 50% of lifetime cycles per battery (bad!). Similarly, charging to a lower voltage (4.1 V/cell) might mean given up 10-15% shots per charge but extending the total life of the battery by a factor of 2.
For more information read
BU-808: How to Prolong Lithium-based Batteries - Battery University