OK, you've stashed your cash. Next it's time to make your way out of the airport. This used to be a positively perilous experience, as you are perceived to be a hapless rich tourist ripe for the picking. Now, since the airport has been modernized for the Olympic Games 2010, it's much more organized. There are no more long lines before the immigration, even the luggage takes less time to arrive. Also it's quite easy to avoid any hassling if they know that you are not easy picking.
If you pre-booked a taxi from Vrindavan, then the driver is in the arrival hall with a sign with your name on it. Simple enough. Follow him to the car. You may be approached by "helpful" fellows who want to put your luggage in the trunk (boot) of the taxi (for some gratuity, of course, 10 rupees or so to do something you don't need done at all). You can shake you head and say "Nay" and if they are persistent they can be waved off with "Nay bhai, chalo!" which means more or less "No thanks and get lost!" and a dismissive hand gesture or two. Watch as the trunk (boot) is closed and locked. Hop in the taxi and you're on your way. The driver may want a few rupees for parking and may want some payment. You can give him max. Rs. 500 in advance to buy diesel.
In general you pay the driver the amount you were quoted on the phone or by the devotee who arranged your taxi when you arrive at the destination. This companies whole business is driving devotees around, so they don't engage in any cheating or funny business, unlike the other taxi wallahs. Still sometimes, the driver will ask for a tip, which you are not obliged to give.
If you come back to Delhi in a taxi, unless you are in an actual taxi (with the word "Taxi" painted on it) the driver may want to be paid a mile before the airport. This is because there is no such thing as private cars for hire and the Traffic Police will want to fine the driver if you are seen paying him there in front of the terminal.
Somewhere along the way, the driver normally stop for breakfast, lunch or dinner at a pure veg dhaba (roadside eatery) on the fringes of Vrindavan dham. This is particularly entertaining when coming from Delhi because it's on the opposite side of the divided highway (dual carriageway). The solution? Drive on the wrong side of the highway for a hundred yards or so, of course! The stop usually lasts about 20 minutes. You might like to take this opportunity to step out and stretch your legs, use the toilet or buy some water or even order a paratha which is ready in 10 minutes. Don't leave your valuables unattended in the car, or ask the driver to lock the car.
If you need to book a taxi in the airport you then proceed to the arrival hall and go to the far left where you find a counter with the sign "Prepaid Taxi". A few years ago the Delhi authorities have made it much safer by instituting strict ban on unregistered taxis entering the airport arrivals area. They have pretty much solved the worst problem, which was getting ripped off or taken somewhere you didn't want to go by a cheating taxi wallah. Still, on the way you may even be approached by a taxi man (taxi wallah), though this is forbidden (they lied and/or bribed their way in to do this). Ignore him. At this DTP prepaid taxi booth you can book your taxi – their prices are fixed. However, booking a taxi to Vrindavan will be much more costly then pre-booking a taxi beforehand which is coming from Vrindavan.