Innsbruck is situated at one of the main European railway routes. So it can be reached easily from Munich in the north as well as from Venice and Milano in the south.
Intercity trains and car trains are the most comfortable way to travel. From Innsbruck you can reach the most important valleys and villages by train, all other places by bus.
More information to the public transport in Tyrol you find here (in German language). Below you find an overview of the railway connections:
NORTH TYROL BY TRAIN:
via Stuttgart - Munich - Rosenheim
via Zurich and St. Anton am Arlberg (North Tyrol)
via Vienna - Graz - Salzburg
via Milan - Trento - Verona via Brennero
EAST TYROL BY TRAIN:
via Bolzano - Bressanone - Sillian - Lienz
via Spittal to Lienz-Sillian
via Kitzbühel - proceed with public transport to Matrei-Lienz
We wish you a safe travel!