Here is a guide on how to use the scenic railway which will connect you to the rest of the High Tatras.
Map of the Railway

Timetable
The timetable is visible at:
https://www.zssk.sk/en/timetables/
You have to scroll to page 214 to find the timetable relevant to Tatransky Leiskovec. There is roughly one train an hour from Tatransky Leiskovec, so don’t be late!
How to buy tickets?
Tickets can be bought online using the the following link
You can purchase single tickets, or day passes. the maximum price for the day pass is €4. They also have discounts if you are under 21 or over 65.