Railway station help required

I will visit Mumbai for first time, my train says it will arrive mumbai at CSMT and I have my work at IITB and my return train says it's from LTT, I can locate it on map, but I don't know about local trains and all, plus I was wondering how is auto to travel between these places(CSMT→IITB→LTT) how should one travel to save time too, and if I take auto/local train can someone tell how much money will it take? Plz it will be helpful