Getting Here.....
There are many ways of getting over here, some very cheap, and some slightly less reasonable! but the choice is yours!
People who come here travel from all over the world..... so generally its hard to list everything... but we will try our best. Check out this god awful paint shopped map of the area..... you will be forgiven for having no clue where things are!!! Its as accurate as you can be bothered to be after 6 beers and no patience!

From Poprad Airport
By far the most convenient place to end up if you are gonna hit all the good resorts. Less than an hour transfer from all of them, you are right in the heart of the Tatra Mountain range. Unfortunately, at the moment the only way to get to this part of Slovakia is to fly to london luton first. London Luton to Poprad with Sky Europe Airlines is the way to go - although a low cost operator, the prices for these flights can be expensive. There are now 4 flights a week in and out of Poprad from London.
Getting to the resorts:
Jasna: from the airport, jump in a cab and head for the train station, or "Stanica" in Slovak. From here, regular trains go to the city of "Liptovsky Mikulas" where you want to head. When you want to go riding, there are buses from the City to resort - try not to get stranded up there at night!...... Alternatively at the airport try to offer a bung to one of the guys in the LM number plated buses.... Companies like Propaganda will help you out if you are truly stuck (but why you would fly all the way there without any way of getting to where you are going is just crazy talk. About 40 minutes from Poprad by Car
Donovaly: Take the train from Poprad to Liptovsky Mikulas, once in LM take bus that is going to "Banska Bystrica" which stops in Donovaly en-route. About 1.5 hours from Poprad by car.
Tatranska Lomnica: You couldnt be closer. The area of the high tatras you will see from the Plane as you come in to land.... about 15 minutes from Poprad. Get to the bus station in town and you are away. Alternatively just take a taxi with your kit to save a hell of a lot of hassle.
From Bratislava Airport (also Vienna)
Generally, Bratislava is the main airport that people will take to get here. Its pretty easy going transfer wise, although a little long. But it can be cheap as chips and most places around the world you can get here or to Vienna (about 40 minutes away from BA) quite easily.
From the airport, either take the bus to the Station about 2euros, or jump in a cab for about 18euros. The station is a throw back from a time when architecture consisted of concrete blocks and imposing, unwelcoming iron bars and people. If you can find the charm in this then you are at home. As with Poprad airport, To get to the resorts, just take a train to either Liptovsky Mikulas (for Jasna, Donovaly) or stay on all the way to Poprad. How simple is that? A ticket will set you back about 20euros. Time wise, expect a good 4 hour drinking session on board a train that wouldnt be too far away from the orient express..... after you have had 10 beers anyway.....
Kosice & Krakow, and any where else vaguely resembling civilization:
Kosice Airport is exactly the same as Bratislava, but in reverse. Its quite easy to get to, and about 2 hours transfer time by train to LM, 1.5 hours from Poprad.........