We travelled to Spisske Podhradie from Levoca, 15 km to the west where we were staying. There are fairly frequent buses between the towns and if you too are travelling from Levoca you can use the busstop just outside the north-eastern side of town rather than walking all the way to Levoca bus station. I think the fares were 20 SKK each.
It's worth asking the driver to leave you off at Spisske Kapitula, an old religious settlement about 1 km outside the town. If you're unsure of this stop or you think the driver has forgotten, just mention Kapitula to one of the locals on the bus and they'll tell you when to alight. The views of Spis Castle from here are excellent though Kapitula is well worth exploring as well. From Kapitula it's a 10 minute walk in to the centre of Podhradie. Before you get to Kapitula keep an eye out for Spis Castle as well - it will take your breath away the first time you see it.
It took us ages to find the bus stop in Spisske Podhradie for the return journey as according to our guidebook (Lonely Planet) buses left from the main square. This was incorrect. We waited for about 20 minutes int he mian square for any bus to pass by but after a while we were getting worried we'd missed the last one. In the end we asked a girl in the local shop and she showed us the way to go. She spoke no English or German, yet she still kindly stepped outside and pointed the way to the bus stop. How nice! The bus stop is about 2 streets west of the main square.
You can easily get to Spisske Podhradie by bus from Levoca. Buses also go onwards every few hours to Presov (1hr) and Kosice (1hr 45mins).
From Levoca, the buses run maybe every half an hour from Namestie Stefana Kluberta, just outside the gates of the old town. Check the timetable in the Tourist Information Office in Levoca.
Buses onwards to Kosice leave from the square by the churchyard round the corner from Marianske nam (pictured).