(sorry to just jump in, I just signed up here. )
A little Ganesh is always good to have around.
Also, now that Diwali (huge Hindu festival in India) is coming up, I'm sure there will be parties and get-togethers and such. Maybe you will be invited to one, and you can experience a bit of the culture that way. Ask questions. People, from my experience, generally enjoy talking about their culture to people that are genuinely interested.
Maybe you could also learn some Hindi or any other language your co-workers speak. One of my American friends is learning a little Hindi and said one word in Hindi that was overheard by someone nearby, who immediately said (and completely in earnest), "You speak very well!"
Oh yeah and don't automatically think that everyone is fresh off the plane.