The national rail service has a good website with schedule information (see below), though it is best to double-check schedule information at train stations in person if possible. In general, trains are more comfortable than buses.
The following are the official websites in English and German from Slovak Railways (ZSR). This gives reliable information for point-to-point travel. You can also check between any city in Europe and the Slovak city of your destination.
ENGLISH: Slovak Railways (ZSR)
GERMAN: Slovak Railways (ZSR)
Here is a quite good website for planning your route: http://cp.atlas.sk/vlakbus/spojenie/ (we recommended use this link)
If you'll travel by bus or train, your destination station in Tatr.Lomnica/Vysoké Tatry.
From Poprad-Tatry Railway station to Tatranska Lomnica Railway station
From Tatranska Lomnica Railway station to Hotel Sasanka