"Question: How do I take care of a Lithium Ion battery to prolong its life? Should I charge it frequently or drain it fully before charging it?

Lithium ion batteries are particular about their operating conditions, and there are a lot of small things that can contribute to better quality of life. Li-ion batteries have a reasonably finite lifespan and can hold only a fraction of their original capacity after a few years, but things like operating temperature, how long the battery spends plugged in, how the battery is used, and the charge cycling you asked about can contribute to how long the battery lasts. If Michael Pollan had to sum up ideal Li-ion battery usage, he might say something like, "Use your battery. Not too much. Mostly for small apps..."