Located to the west of the city of New Delhi is the Indira Gandhi International Airport, which now is the busiest airport in South Asia. There are now two termimals T3 and T1D which are eight kilometers apart. So budget at least 30 minutes to get to T1D if you have to catch a connecting flight within India.
You can either take the free shuttle from the new international terminal, nicknamed T3, near Pillar 9 or take a pre-paid taxi from the same location.
T3, the brand new international terminal built in 2011, is equipped with all the amenities an international traveler needs - a huge variety of duty-free shopping that is available to inbound travelers as well as to outbound, currency exchanges offering reasonably good rates, Airtel sim cards in case you want to turn your unlocked overseas cell phone into an Indian cell phone while in India, little rooms for sleeping off your jet lag, even "wave chairs" on which you can recline almost 180 degrees and catch a nap, and loads of restaurants catering to all tastes. 

Currently, international visitors will arrive at the Delhi International T3. This terminal also has a domestic wing catering to flights inside India. In case you have a direct flight to catch within India post your arrival, you can transfer immediately from International Arrivals to Domestic departures. However only the following domestic airlines operate from T3 (Kingfisher, Jet Airways, Jet Konnect, Indian and Air India)

However this will not work if your domestic flight within India is with a low cost carrier such as Indigo, Spice Jet and Go Air. All these airlines operate from the old terminal T1D. Getting from T3 to T1D will take around 30-40 mins depending on the traffic situation. 

Note: Indigo and Spice Jet are primarily domestic operators running some international routes. So in case you have a Indigo international flight, you will have to take it from T3 and in case you have a Indigo domestic flight, you will have to take it from T1D. The basic logic being that T1D does not support any international traffic and has no immegration facilities. 

The web site for the airport is: Indira Gandhi International Airport (DEL) New Delhi

There are various modes of transportation from T3 to the city: 

1. Metro now connects the airport to the heart of the city. One you arrive at a metro station in the city,  you can hail a cab to wherever you need to go. If you are carrying no more than a suitcase and a handbag, the metro is a smart way to get to the city for USD 50 cents or less. From the station, a 3-wheeler to anywhere within 2 or 3 kilometers is probably less than Rs. 100 (about USD 2.25).

As of April 2013 the METRO is up and running. Catch it from the airport and get off at New Delhi. As you walk out of the Metro you will sight the New Delhi train station. Walk and enter. Turn to left and climb the stairs. Turn right and you are on the overhead bridge that connects all 16 platforms of the station. You have entered from the No.16 end so walk to the other end to get at No.1. Exit is from here. As you look out with the train station at your back you will see Paharganj on the other side of the road.

2. Prepaid taxis (Black and Yellow colored) are available at a booth inside the arrival as well as Two both outside on Taxi bay of T3, the international terminal, as well as from the domestic terminal T1D. These taxis will drop you at the doorstep anywhere in Delhi and are probably a better option than #1 for the uninitiated. The prepaid taxi booth has a menu of all the major destinations with the approved and fixed fare for each. There is no risk of a rip off because you are charged a fixed government approved fare for the trip. you can hire the AC and non AC cab. generally by 25% Extra you can go with  the AC cab. also note that between 23:00 hr to morning 05:00 Hrs there is 25% extar night charge would be applicable on both AC An Non AC taxi.  It is cheap. For less than Rs. 300 (about USD 7), you are home! 

There is a pre-paid taxi counter inside the arrival lounge to the extreme left when you are arriving from the international terminal. (This is after customs. This lounge serves as an intermediate space between the final arrivals area).  They will ask you for the adress of the place and give you two receipts. You can then leave the building and go to pillar 34-40 when you leave the terminal building. There is an additional counter here, in case you miss it inside, and all the yellow-black taxis are parked here. Once here, you can tell the drivers the address you need togo to, and they will figure out the car that you are supposed to take. You are supposed to finally hand over the reciept to the driver only after you reach the destination, so you can ask to have it back if they need to check it. This is definitely very convinient and a cheap option. A 3 AM trip to the Old Delhi Railway Station with two large bags cost INR 485 (about USD 10), and took about 40 minutes. 

3. Metered Radio taxis are a little more expensive than prepaid taxis described in option #2 ad are lined up in front of the terminal building as in any airport in the world. They are run by some private companies such as MERU, EASYCABS, QUICKCABS, etc. One is told prepaid averages Rs 14 per km for Non AC  & Rs 16/- per KM for AC one vs. Rs 20 of metered cars. Regardless of the slightly higher cost, these metered cars are later model cars with AC and probably worth the few extra dollars in the searing heat of a Delhi summer. There is a official Rs. 80 airport parking charge that the Radio taxis have to pay which in turn you have to shell out, but Rs. 80 for parking (about USD 1.90) isn't going to break your budget. This will be a charge over and above the number you see onm your meter at the end of the ride. So grin and bear it. If you spend USD 7 on a pre-paid taxi, you might spend USD 12 on a metered cab - not a big deal by global standards. You can also compare the prices of taxi and check for offers at http://www.taxiclues.com before booking a cab. 

4. There are A/C buses available to a few destinations including the major railway stations and bus stops. These buses have few stops and few passangers, so they take little time. The Inter State Bus Terminus(ISBT) at Kashmiri Gate has a very ferquent bus service. The tickets can be a little pricey thouhg, and for 2 people, a pre-paid taxi may work out cheaper. These buses are available towards the extreme right of the arrivals area. 

 Options to the airport are as follows:

1. Of course, the cheap metro option still applies whether departing or arriving.

2. The pre-paid option does not exist from the city..

3. The metered taxis as described in #3 above can be called anytime, anywhere. Try Meru cabs or Mega cabs. Meru's number is 011-442-24422.

Try not to use the transportation so courteously "arranged" by the hotel. They are horrendously expensive. A Taj hotel recently quoted a price six times that of what a metered cab would have charged, all for the privilege of not having to talk to a local.

Getting to New Delhi Railway Station from T1D 

This option would be required if you arrive in Delhi in a low cost carrier on a domestic route (Indigo, Spicejet and GoAir). Once you land at T1D, there is a Pre Paid Taxi counter (Black and Yellow cabs). The process to get the reciept is the same as decsribed above and you can book the taxi to New Delhi Metro station directly.

There is also a booth outside the main terminal building which seels the Metro Tickets for the Airport Link to New Delhi. However, note that the Metro Station is at T3 while you are at T1D. if you buy the ticket from this booth, you are eligible to board a shuttle which will take you from T1D to T3 (around 8kms and 20-30mins) free of cost

Once you get to T3, follow the instructions to reach the Metro station and then find yourself on your way to New Delhi Railway Station Metro Station

 Getting into the Airport - Ticket Printouts Update

The Indian Government has recently passed a resolution aimed at saving paper. As part of this resolution, across all airports in India, you no longer require a paper printout of your itinerary. The itinerary document on your smartphone, ipad, kindle, etc will be sufficient to get you inside the airport when paired with the correct ID Proof.