Most bus services between larger towns and villages are now run by Stagecoach (www.stagecoachbus.com), with a number of smaller coach companies offering infrequent services to other areas. Dartmoor is poorly served by buses; you'll need a car or bike to access its more remote areas.
There are several bus passes available: the Devon Day Ticket (adult/child/family £9.30/6.20/18.60) covers all companies, while the Stagecoach South West Explorer (adult/child/family £8.30/5.50/16.60) and South West Megarider Gold tickets (one week £30) only cover Stagecoach buses. Check the Stagecoach website for details.
Traveline South West (www.travelinesw.com) is a great online tool for travel planning, while the Devon interactive bus map (https://new.devon.gov.uk/travel) provides a useful visual map of bus routes.
Devon's main line skirts southern Dartmoor, running from Exeter to Plymouth and on to Cornwall. Branch lines include the 39-mile Exeter–Barnstaple Tarka Line, the 15-mile Plymouth–Gunnislake Tamar Valley Line and the scenic Exeter–Torquay Paignton line. There are also several lovely steam railways.
The Freedom of Devon & Cornwall Rover ticket (three days travel in seven days adult/child £49/24.50, eight days travel in 15 £79/39.50) is good value if you're using the train extensively.