With this address www.db.de
you are able to plan your train ride anywhere in Europe - it's "Die Bahn", the German Rail (I'm Danish myself, working in the danish rail and we only use this site to plan travelling in Europe).
And there are no trains to Cortina.
and this www.dolomitibus.it
are sites covering most of the Dolomites area with busses.
which is the Club Alpino Italiano you will be able to find for instance huts (rifugios) all over Italy.
Concerning maps I also prefere Tabacco - they are very accurate topografical maps of the Dolomites, best 1:25.000.
Remember, if you go by car you always have to get back to get the car. If you don't have a car you will be able to follow one of the fantastic routes - the Alta Vias 1-8 or so - for just a few days, or several weeks. Alta Via means The High Route, and they follow high tracks from hut to hut. The huts are either private or owned by the CAI, and they are all very beautiful situated and well run with all necessities for the relaxed life in the mountains.
Here is a page about many useful things in the Dolomites www.dolomiti.it
I hope this helps you some of the way to the most beautiful mountains in the world.