Obviously as you mention the tanpura plays a very important role in anchoring the tonic for other musicians. In addition to establishing the tonic it can add color in other ways...the usual tuning is with one Pa string and three or more Sa, but some raags will use a Ni which adds a very beautiful color, and the "pa-less" raags use some interesting tunings on occasion, often centering around Ma. One interesting tuning I heard on a Nikhil Banerjee recording (Hemant) was Ma-Dha-Sa'-Sa, it was really hard for me to not hear it as Sa-Ga-Pa-'Pa. Different instruments require the tanpura in different ways. For vocal ICM it seems all but essential, and for tarab-free instruments like the rudra veena in dhrupad it seems fairly constant. I've noticed Maihar gharana sitarists tend to use them a little more commonly than Etawah gharana. Ust. Imrat Khan told me the gandhar pancham tuning of his brother had a sort of, as he said, "built-in tanpura" in the chikaris and quite often they will perform just with tabla, no tanpura, although I've seen several videos where there were two tanpura players on stage with Vilayat Khansaheb. Although I wonder if sometimes it is more for looks, particularly when the players are female!
Sometimes I will play my tanpura (Rikhi Ram instrumental style) for grins by itself, and hum softly on a raag. I'm no singer by any stretch but it is nice to play tanpura and sing a bit. Certainly it can be very relaxing to play a well adjusted, resonant tanpura. Definitely feels more alive when the dandi is resonating next to your head, than say, a recording of a tanpura or a tanpura machine being played.
As far as how to know how to play it I imagine most string musicians will adjust to it easily...coming from a bass background the finger plucking technique is very natural for me, but when my wife tried (she played flute) she had a hard time getting a smooth, soft sound from the strings, so it might take a bit of practice for a non-string player. Keeping it in tune might be a bigger challenge!