Glastonbury lost its railway station in 1966 and has not had one since, which makes getting there slower than you would expect for somewhere so famous.
By train. The nearest station is Castle Cary, about 12 miles east on the line between London Paddington and Penzance. From there, a taxi to Glastonbury runs about £20-25. Bath Spa station, with frequent trains from London, Bristol, and the south coast, is connected to Glastonbury by Mendip Xplorer and First Bus services taking about 90 minutes.
By bus. First Bus 376 runs from Bristol bus station through Wells to Glastonbury in around 90 minutes, every 15-30 minutes during the day. The 29 connects Glastonbury with Taunton via Street. The bus station is just off Magdalene Street, a few minutes' walk from the Abbey.
By car. Glastonbury is about 130 miles west of London, 30 miles south of Bristol, and 30 miles south-west of Bath. Pay-and-display car parks are scattered around the town centre; the Abbey, Tor, and Chalice Well each have their own. The Tor itself can only be reached on foot from one of two parking-and-walking points.
Festival week. All conventional transport groans under the strain. Many festival-goers arrive by coach direct to the Worthy Farm site; if you are visiting the town itself, expect heavy traffic on roads in and out.