Night or day New Delhi does not sleep, so no mater what time you arrive don't worry chicken curry things will work out. At least you hope!
From the airport you can take a taxi or airport bus to Paharganj and the Main Bazar. Typically a traveler will buy a ticket at the pre-paid taxi booth located inside the terminal. You will need some local currency for this. You can change money at some banks but they typical give a poor airport rate, so just change about $50. You can also find an ATM. iF you luggage is delayed you can use the time to change money.
The prepaid taxi will cost 425Rs if you are going to the Main Bazar or Paharganj Rd. You can also walk out side of the airport terminal and there will be many taxi there who are returning with out a fare, and will take you for a slightly better rate, around 280Rs.
Airport Bus service is available and will take 45 minutes to 1 hour to reach the New Delhi Railway station, the bus will also pass by Connaught Circus. The bus it not too bad because it offer air condition and is overall not a bad alternative to a taxi. Fare is 65Rs.
If you have a flight the next day you may want to stay at one of the many hotels near the airport. You need to get out of the airport then take a rickshaw a short distance across the highway.