By train
Major train routes pass into Styria from all neighbouring provinces and countries. There is an hourly Inter-City connection to Vienna and Carinthia as well as regular Inter/Euro-City connections to Linz, Salzburg and Maribor
By bike
There is an excellent bicycle route available next to the river Mur. It starts in Salzburg and ends at the border to Slovenia, at Spielfeld you can cross the border to Slovenia and from there use the bicycle route 1 to get to Maribor.
There is also a possibility to get to Styria using the Drau bicycle route from Tyrol and Carinthia, either via Maribor or via another bicycle route at the very south of the Styria/Carinthia border that crosses over to the Mur bicycle route.
By bus
Postbus is operating a route from Klagenfurt to Graz which is significantly faster than the train.
Eurolines operates a few international destinations from/to Graz.
Otherwise it will be difficult to find a long distance bus leaving to Styria.
By car
Motorways A2 from Vienna to Carinthia and A9 from Linz to the slovenian border cross at Graz. There is also a major route available from Salzburg EnnstalbundestraÃe.
On foot
The european hiking route "Fernwanderweg" E4 alpin starts in Andalusia, Spain crosses through Styria and ends in Crete.
The Austrian hiking routes "Weitwanderweg" 01, 02, 03, 05, 06, 07, 08, 09 cross through Styria as well.