Get to Varanasi. There is a small regional airport with domestic flights. However, if Varanasi is part of a larger tour of India, you will probably be arriving by train. The city is on the rail line between Dehli and Kolkatta, and only a short journey from Agra and the Taj Mahal. Avoid travel by bus in this part of India if you can, as both the vehicles and the roads are unreliable.
Find a hotel near the Ganges. Taking in the spiritual center of the Hindu religion is the main reason for coming to Varanasi, so not being able to walk there is a big minus. Also, taking a taxi or hotel shuttle down to the Ganges paints you as a mark for every beggar and scam artist who sees you get out.
Tour the ghats. The best way to explore the Ganges riverfront, with its temples, steps to the river (ghats) and crematory platforms is on foot. It is a ghostly experience, and there is nothing quite like it anywhere in the world. Just remember to be respectful, and never try to photograph a cremation. Try taking a boat ride and seeing the ghats from the river too.
Visit Vishwanath Temple. Sometimes called "the Golden Temple," it has this other name because its 45-foot spire is decorated by one ton of gold. Like taking a bath in the Ganges, visiting this temple is part of every Hindu's pilgrimage to Varanasi.
Try to find a sadhu who speaks English. Some of these (in)famous Indian ascetic holy men are quite accessible, but don't push it. If they cannot or do not want to talk to you, respect their privacy.
Hire an auto-rickshaw and head out to Sarnath. While it will seem rather modest compared to Varanasi, Sarnath and its ruins are a major holy site in the Buddhist religion. Many of the local temples, each a representative of international Buddhism (Thailand, Japan and Tibetan) are worth visiting while you are there.
Revisit the ghats at night. Hindus on puja often put butter lamps into the Ganges after sunset, creating a scene worth seeing.
Explore the warren of alleyways behind the Ganges. This chaotic, bustling, claustrophobic urban world will reveal some of the best and worst that India has to offer.