You can reach Strbske Pleso in over an hour from Poprad by the Tatra train. In 2007 it cost 40 SKK one way. The trains run roughly every hour.
Instead of buying a normal return ticket from Poprad, you could buy a block ticket for 76 SKK. If you plan to hop on and off all day long on the red Tatra trains, then you may consider buying a daypass for 100 SKK and if you want to use the cog railway too, then choose the one for 120 SKK.
There is a kiosk and clean pay toilets in the station building.
From Poprad or Bratislava direction you can also get off at Strba from the national railway and catch a cog railway up to Strbske Pleso. A one way ticket cost in 2007 SKK 30.