There is no direct bus operating at Varanasi Lal Bahadur Shastri Airport.
The only bus option is to walk to Babathur crossing and then take a state-run bus to Varanasi Junction Train Station. The station is located 4 km away from the city center; there, you should take a rickshaw (tuk-tuk) get to city center which will cost around INR 120.
The bus ticket costs around INR 30 and the whole trip takes around 90 minutes.
You should consider this option only if you are super tight on budget. The buses are extremely crowded and uncomfortable.
There are no metros or trains connecting Varanasi Lal Bahadur Shastri Airport (VNS) to Varanasi city center.
Taxi is the only option to get directly to the city center. There is a pre-paid taxi counter right next to the baggage claim area where you can book a taxi.
The trip to Varanasi center takes around an hour and the cost is approximately INR 700.
You can also get a rickshaw, however the trip will take around 2 hours and the cost will be around INR 500. We do not recommend this option; it is quite uncomfortable and dangerous as the traffic between the airport and the city center probably one of the worst you would find in India.
Varanasi city center is pretty much the only destination for incoming travelers. Simply find some other travelers to share a taxi.
Avoid getting a non-official taxi at the airport for security issues. In any case, your driver may want to take you to another hotel or may say that your hotel is fully booked or has burned down, in order to take you somewhere else. Just ignore this and insist on going to the hotel you've booked.