Travelling from Innsbruck airport you get the bus just outside the SMALL terminal and 20min later at the rail station. You then need a train (every 2hrs but seat reservation compulsory) which typically is going to Verona or Milan or Venice, but you need to get it to Fortezza, then you need another train from Fortezza to Dobbiaco, and a bus from there to Cortina. (The railway to Cortina was closed years ago) Overall journey time is about 3 hrs. For all arrivals of the train at Dobbiacco there is a connecting bus service down to Cortina (another 35 minutes): for some arrivals it would be a 2hr wait. There doesn't appear to be any other way, a local thought a taxi would be very expensive, there is a station buffet, bar to sit in and some other hotels and other buildings about 150 yds away from the station so you could sit it out after pushing your bags.

Remember in winter time the flight may be delayed so prebooking a rail reservation may be wasted, so you gamble on seats being available at Innsbruck rail station- though it seemed there were plenty of seats and some travellers didnt seem to know they had to have a seat reservation! Also the train is coming from Munch so it could be delayed, you have to change trains, it is possible to do if you wish......

Also though the trip from Austria up over the Alps into Italy could be spectacular, through the historical Brenner Pass etc  it was more scenic than spectacular, nice then, the train for an international one was not particularly new either so no romance here, and the place noted in WW2 negotiations was just a stop for the Austrian and Italian rail staff to swop over. 

Leaving Cortina for a stay in Venice. You get a local bus from the centre to Calalzo about 60mins away which is the southern nearest railway station and then the train which was nice to go straight into Santa Lucia Rail station (Venice) and straight in front is the grand canal. Trains also stop at Mestre, the last stop on the mainland before Venice. Takes the rail about 2.5 hrs though and this was the quick one of the morning , there are others during the day but they take even longer. Remember in winter the snow as the roads can be delayed and arrivals can be late at the rail station!

Cortina Express is the only direct coach line service, which connects Cortina with Venice Airport and Mestre Railway Station in just 2,15 hour. The service is available all year long, every day. On one or two days per week this express coach stops at Treviso, the airport used by low-cost carriers including Ryanair. In Mestre railway station you will find the best connections to other Italian cities by high speed trains. Info and reservations, tickets on line on their web site