NOTE: In Bengali "Rickshaw" is pronounced "Rish-kaw". Try not to laugh too much when the time comes.
When dealing with rickshaws or autorickshaws you should always try to find out the going rate, because the divide by two rule won't do much good if they quote you five times the going rate. You are in a position of strength when there are a few (or a lot) of rickshaws around. They generally give in pretty quickly when you start walking over to the next guy especially if there aren't a lot of potential customers around.
With all rickshaws, you fix the price before you get in which generally involves some bargaining. Tell them where you want to go and ask how much. The Hindi word for "How much" is "Kit-na?" As in "Railway booking office at Fairlie Place, Kit-na?" (well, that's not quite proper Bengali, but "Kit-na" works fine). Being a tourist you will always pay more, but should not pay outrageously more. You're expected to haggle a little bit using the strategy described above. Knowing the going rate is key. Sometimes (not often) the rickshaw wallah will actually quote the going rate, in which case there's no need to haggle, jump in and say "chalo bhai!" (which can mean "Get Lost", but in this case means "Lets get going!")
Knowing the Bengali numbers from one to fifty is handy too. You might consider picking up a copy of the Lonely Planet Bengali Phrasebook. Unlike Delhi, many Bengalis only speak Bengali well, especially in Navadvipa, though generally they will understand you if you attempt Hindi. There are some differences between Hindi and Bengali pronunciation. The consonant "V" like "Vamana Dev" is always pronounced as "B" so it becomes "Bamana Deb". Generally the hard consonant "A" (the short a) sound in Hindi is replaced by "O". If you were to speak Hindi with a mouth full of marbles, you'd have Bengali... mostly.
For getting around Kolkata a taxi is probably your best bet. There is an efficient and cheap underground Metro (8 AM - 9:15 PM Mon-Sat, Closed Sunday). It runs north to south through the center of the city, but to get to the railway booking office or other places, you will still need a rickshaw or taxi.
Auto rickshaws in Kolkata mostly operate on a shared basis, where several passengers pay a fixed rate to share the auto which runs on a fixed route.
Kolkata is also the home of the world's last hand drawn rickshaws.