If you're not being met, and are headed for the train or a hotel (see below) then your first stop is the Delhi Traffic Police Prepaid Taxi Booth, which is located just outside the customs on the far left side of the arrival hall. Taxis are available 24 hours a day. There used to be a huge crush of taxi wallahs to pounce on you immediately outside the arrivals door. Since then, they have instituted a different system and no one should approach you before you get to the DTP booth.Still it may happen, so be prepared.
If you are at all in devotee dress they will surmise your destination "Hare Krishna! Vrindavan? Mathura? ISKCON ISKCON?". Ignore them and keep walking. The DTP booth exists because the Delhi taxi wallahs are inveterate liars and cheaters. By dealing ONLY with the DTP booth, you won't get cheated or taken someplace you don't want to go (like a hotel that will overcharge you massively and split the booty with the taxi driver). Ignore whatever comes on your way, wait your turn, and tell the DTP officer where you want to go and pay the fare, which is a fixed rate based on distance plus a small charge for extra bags. The details are on the DTP web site. The current system at the airport is a very great improvement over the old system. They take your name and write the last four digits of taxi registration number on the prepaid receipt, making it very easy to trace any complaints. When you get the prepaid voucher, the DTP officer will tell you the taxi number. You then go outside to the taxi rank across the street and find the right taxi. It will be somewhere near the front of the queue. Then match the number on the voucher to the license plate on the front of the taxi. When I arrived my number was "2060" which corresponded to a plate that was "DL 99 2060" or some such number. It took a minute to find the right taxi, since at about 3 AM they were not very alert. The taxi wallahs know their numbers and are able to assist you, just check the number on the front to be sure. The way the prepaid arrangement works is you get a piece of paper from the DTP officer which you give to the driver when you reach the destination. There is only one exception to this, which is just as the taxi is leaving the arrivals area, they are checked by a DTP traffic officer, who will need to see your paper, just for a minute. The driver should hand the paper back to you immediately when he is cleared to leave by the traffic officer. Put the piece of paper in your pocket and don't take it out. Give it to the driver at the very end and not before.
The airport troubles have been thouroughly addressed, though in other parts of Delhi, you will need to be more cautious when dealing with prepaid taxis and especially auto rickshaws. When you arrive at the taxi or auto rickshaw, write down his taxi number on a piece of paper and make sure he sees you do it. Depending on the time of day, you may need a flashlight (torch) to do this with the appropriate flair. Read it out loud once or twice and don't explain why you're doing it. This act may save you from ending up at a different place than you want to be taken. Since you have his plate details, you can lodge a complaint with the Delhi Traffic Police. If somehow you don't end up where you want to be (his favorite hotel) or get told a pack of lies about riots, hotel full, hotel burned down, etc. then you can tell him "I have your taxi number and I will report you to the Traffic Police and they will beat you!" And they will, too. That will cause him to say "OK OK" and take you to the right place.
