What are the ways to travel from Delhi to Varanasi? And how long does each route take?
One can use any of the following 3 ways to travel from Delhi to Varanasi. 
1. Travel by flight from Delhi airport to Varanasi.  Depending on where you stay in Delhi, your travel time to Delhi airport could be between 45 mins to 2 hours.  The flight time from Delhi to Varanasi is 1 hour 30 minutes.  On arrival at Varanasi airport, it takes about 1 hour to get to the city.  The total time that this route takes is about 7- 8 hours taking into account the airport security time. 
2. You could take a train from New Delhi railway station to go to Varanasi.  The fastest train travel time is about 6 hours and the Varanasi railway station is in the heart of the city.  The total time this route takes is also between 7-8 hours depending on how far one is from the New Delhi railway station. 
3. The last option one could consider is driving by road from Delhi to Varanasi.  The total travel time by this route is bout 11-12 hours with a couple of breaks on the way.