The nearest airport is Kolkata, though flying from Europe it is generally a lot less expensive to fly to New Delhi and take the train to Navadvipa. Flying from the west coast of America the price difference between New Delhi and Kolkata is not as great. As with all times of the year flying to India it is wise to book well in advance and book a return date.
The best place to buy tickets are from travel agents specializing in travel to India. These places buy their tickets from consolidators, and their prices are always lower than internet travel sites (except maybe Priceline) or regular non-Indian travel agencies. Any Indian grocery will have advertisements for these agencies. They are located in all major cities, and are happy to deal with you wherever you are as long as you are in the same country. It pays to shop around (everyone does it) so don't feel pressured to make a booking or buy the ticket on the first call.
Prices depend on the airline, the routing, the season, and how long the ticket is valid. Open tickets (with no fixed return date) are risky, as the flights from India are always fully booked, it may take weeks to get a confirmed reservation out of India. Generally you can fix a date and change it later without penalty. Check with the travel agent or the airline. Sometimes the cheapest tickets must be purchased months in advance. I have had several bad experiences with Air India and would suggest giving them a miss.
Before you leave for India, find out the phone number for the airline in New Delhi (it may have changed recently). The best place to find this out is the airline's web site.
Once you are in India, it is imperative that you reconfirm your ticket. All you have to do is call them up and confirm the you are leaving on the flight that you had booked. It seems unnecessary, but travellers often change their plans without changing their tickets (leaving a lot of empty seats) which is a problem for the airlines. You have to reconfirm a minimum of three days before departure from India. You can do it the as soon as you arrive, and if you stay in Delhi for any time it would be easiest to call the airline from there. There are travel agents in Vrindaban and Mathura who can reconfirm it for you for Rs200 or so. Even with reconfirmation the airlines routinely overbook their flights, so if you really want to fly on the day you booked, arrive at the airport at least four hours before departure.
If you fly Turkmenistan Airways they would like you to come to their office in New Delhi to reconfirm your ticket. Since this is absurdly inconvenient they will also allow you to fax your details to them for reconfirmation. You will need a photocopy of your return ticket, the photo page of your passport, and the Indian Visa page of you passport. Most other airlines don't require any of this and a simple phone call will suffice. The number for Turkmenistan in New Delhi is is 2372-1085 and the fax number is 2331-8249. It is less expensive and a time savings to reconfirm in New Delhi since it is a local call. It cost me Rs. 2 to call them (local call) plus Rs. 3 for photocopies, and Rs. 34 to fax the three page to them. In all it took about ten minutes to reconfirm, since the STD office had a fax, and photocopies could be made just across the street.
I've bought a few tickets from Radha Travels in New York City (212-719-3244) and they are OK.
Bharata Travel (also in New York City) (212-889-7511, ask for Chinmoyee) comes recommended.
According to one devotee from Los Angeles, the two best travel agents in LA for going to India are:
Town and Country Travel Agent
Phone: (323) 464 1214.
Address: 6603 W Sunset Blvd, LA, CA 90028.
Mr. Ravi is the owner and they offer the best 1 year ticket.
Phone: (310) 836 1477.
Address: LOS ANGELES, CA 90001 (don't know the exact address)
Most devotees use this one, and they have some good deals.
The cheapest airlines from Los Angeles are China Airlines and China Eastern Airlines.
In England, Travel Connection in Wembley (0181-900-0292) is recommended.