There are connections from Prague and Liberec, but you will have to change trains several times.
Buses are leaving from Prague almost hourly. These are main bus lines:
Prague - Korenov - Harrachov
Prague - Jilemnice
Prague - Vrchlabi - Spindleruv Mlyn
Prague - Trutnov - Pec pod Snezkou
You can reach the eastern part of the Krkonose Mts. from Hradec Kralove and western and central parts from Liberec as well:
Hradec Králové - Trutnov - Pec pod Snežkou
Hradec Králové - Vrchlabí
Liberec - Harrachov - Jilemnice - Vrchlabí.
You can find suitable connections on web site www.idos.cz.
We would be pleased to help you with your travel. Simply mail us your arrival time in Prague or Liberec and we will find adequate bus connections for you. firstname.lastname@example.org