There is a regular Hobart airport bus service that connects with all arriving and departing flights. There are pickups and dropoffs around downtown. The journey time is about 30 minutes.
There are no regular passenger trains in Tasmania, but you can travel from Hobart to Launceston on Redline coaches. Redline operate a handful of services along Tasmania's main highway route each day. The journey takes about 3 hours.
You can travel from Hobart to Melbourne by Redline coach departing Hobart in the early afternoon, getting you to the ferry terminal in East Devonport in the afternoon, then boarding the Spirit of Tasmania ferry for the overnight sailing across Bass Strait before arriving in Melbourne the following morning. You can then catch a No 109 tram from Station Pier Port Melbourne to downtown.
Check out our list of train journeys from major Australian Cities. Each page has links to timetables and online ticket booking for journeys to country and interstate destinations.