International travelers arriving by air will land at Chattrapathi Shivaji International (BOM) Airport . Mumbai Airport has two terminals. The international is terminal 2 aka Sahar and the domestic is terminal's 1A & 1B aka Santa Cruz.
Most international flights in Mumbai arrive late in the late evening. The BEST's bus number S-3 runs at these times ferrying passengers from the airport to the Fort, Fountain and Colaba Areas. If you're getting your own taxi it's best to take a pre-paid cab, it will cost more but they are pretty reliable. These are government-approved taxis and will have fixed rates for different locations in Mumbai. The maximum distance charge in Dec 2006 was R420 plus baggage charge R5 per bag for an air conditioned cab which may be several decades old. The fare is paid at a kiosk and then you have to find the taxi that is given on the chit. Do not let one of the "porters" try to take your bags/trolley. They can get very demanding for a tip for wheeling your trolley no more than about 50 metres and for which they insist on the tip being paid in dollars, pounds or euros.
If you're taking an independent taxi try to negotiate the rate up front, and make sure the driver understands where you want to go. If you can't negotiate the rate in advance, ask to see the driver's meter conversion card, which he is required to have. Also, make sure he turns the meter on when you get in the car. And if you want a taxi with air-conditioning that will cost you more. Lastly, carry a bunch of 10 Rupee notes and 5 rupee coins, so you have exact change to pay a taxi driver.
Travelers by train (Central Railway) will either arrive in Victoria Terminus, Dadar Terminus or Lokmanya Tilak Terminus (Kurla). Western Railway Terminuses are located at Mumbai Central and Borivili. The Kurla and Borivili Terminuses are at least 1-1.5 hours away (by Taxi) from the prime tourist areas of Fort and Colaba.