There are three ways to reach Vrindavan from New Delhi - bus, cab and train. Out of them, the most convenient one is via taxi (cabs) and the most economical one is via bus.
Metro & Bus
From New Delhi Airport Metro Station or New Delhi Railway Station Metro, all you have to do is to take a metro to Delhi Sarai Kale Metro Station. Just get down here, and you will find buses to Mathura. Just hop into it and it will take around 3 hours for the bus to drop you at Chatikara. From Chatikara, the autowala will charge you 20 rupees to drop you at ISKCON Main Gate. From here, any part of Vrindavan is hardly 2-15 minutes by e-rickshaw.
Travel Time: Around 4-5 hours
Cost: 180-250 rupees (Most economical)
Note: Metro runs from 5 AM - 11 PM. Buses are available from 6 AM - 9 PM. Plan your trip accordingly if you plan to come via bus.
Taxi
You can book a taxi from 'Make my trip, OLA or by local travel agents. Try not to come on weekends (especially Saturdays and Sundays) as there is a huge rush of local devotees from Delhi. Many people come here to spend weekends hence the traffic police put up barricades at most of the entry points. You will have to encounter a lot of traffic jams in Vrindavan and have to park your vehicle at Parking, which is around 1.5 Km from main Vrindavan. Try not to come on weekdays or even Friday nights. Rest of the days, there's hardly any traffic except for important festivals, when again it's a full rush.
Travel Time: Around 2-3.5 hours
Cost: 2500-3500 rupees
Railway
Many trains are available from New Delhi as well as Hazrat Nizamuddin Railway Station. Just hop into any (with or without reservation) and it will take just about 2-3 hours to reach Mathura. From Mathura, you will get regular auto for Vrindavan.
Travel Time: Around 2.5-3.5 hours
Cost: 70-350 rupees (depending upon General, Sleeper or AC Class)