Taxis are a quick and comfortable way to get around in Bangkok, at least if the traffic is flowing your way. All taxis are now metered and air-conditioned: the hailing fee is 35 baht and most trips within Bangkok cost less than 100 baht. There are no surcharges (except from the airport), even at night; don't believe drivers who try to tell you otherwise. A red lit sign on the front window means that the taxi is available.
When the meter is switched on you will see a red '35' somewhere on the dashboard or between the driver and you. Be sure to check for this at the start of the ride, as many drivers will "forget" to start the meter in order to overcharge you at the end of your trip. Most will start the meter when asked politely to do so (meter na khrap/kha (male/female)); if the driver refuses to use the meter after a couple of attempts, simply exit the taxi. In some cases, late at night and especially near major tourist districts like Khao San or Patpong, you will need to walk a block away to catch a meter cab. The effort can save you as much as 150 baht. This is often also the case for taxis that park all day in front of your hotel. The only two reasons that they are there: 1) To take you places where they can get their commissions (Jewelry stores, massage parlors, etc) and 2) To overcharge you by not using the meter. Your best bet is to walk to the road and catch an unoccupied metered taxi in motion (easier than it sounds, as Bangkok traffic tends to crawl the majority of the time, and one car out of four is a taxi). Avoid parked taxis altogether, and if a taxi driver refuses to turn the meter on, simply close the door and find one who will. If they say the meter is broken, a good tactic is to turn it on for them. Keep in mind that it is illegal for them to have unmetered fares. Be smart and give your money to honest drivers, not touts. The only reason they get away with this so frequently is because foreign tourists let them.
Be sure to either know the correct pronunciation of your destination, or have it written in Thai, as taxi drivers in Bangkok are notoriously bad at reading maps. Most hotels and guesthouses will happily write out addresses in Thai for you. While most drivers will recognize the names of tourist hot spots, even if grossly mispronounced, it is often difficult to properly pronounce addresses in Thai, a tonal language. If your mobile phone works in Thailand, it is sometimes useful to phone your hostel and ask the staff to speak to your driver in Thai.
If you're pinching pennies or fussy about your means of transportation, you may wish to think twice before getting into one of the (very common) yellow-green taxis. They are owner-operated and of highly variable quality, and occasionally they have rigged meters. All other colors belong to large taxi companies, which usually enforce their standards better.
On some routes, the driver will ask if he should use the Tollway - this will usually save a lot of time. You have to pay the cost at the toll booth (not in advance, and not at the end of the journey). Watch how much the driver really pays, he may try to keep the change.
When getting out, try to have small bills (100 baht or less) or expect problems with change. Tips are not necessary, but are certainly welcome; most local passengers will round up, or leave any coin change as tip.