The Slovak Paradise (North Part) lies close to the main Slovak train route Bratislava-Kosice. All trains stop in Spiska Nova Ves.
There are a lot of trains between Bratislava and Kosice. Some direct trains from Prag arrive in the station of Spiska Nova Ves as well.
Traveling from Poland
The best way to get there by train is via Katowice. A direct train takes you to the city called Zilina on the Slovak main train route where you can catch a train to SNV. If you miss the direct train you can try to catch a train going to Zwardon. Some Slowak trains cross the border to Poland and go back. Check the best connections before you get on the train in Katowice.
Traveling from Hungary
If you are going to travel from Budapest go via Kosice. It's faster, easier and cheaper than via Bratislava.
Traveling from Czech Republik
It's easy to travel from Prag or other Czech cities. A lot of connections.
Some ticket prices:
Zwardon (PL) - Spisska Nova Ves - 290 km - approx. 10€
SNV - Ruzomberok - 180 km -approx 5€
SNV - Spisske Tomasovce (a train station close to the Slovak Paradise) - approx. 0,40€ /only regional trains/
Cingov, a small hamlet on the north-east of the park, was our entry point to Slovensky Raj. Cingov is There are a few hotels, an information board, a couple of shops and not much more. Numerous interesting trails start from here, which is why we had chosen it as or starting point. The nearest town to Congov is Spisska Nova Ves, about 5 km away and there are buses between the two, but not as many as you might expect. Spisska Nova Ves is on the main rail line between Bratislava, the Tatras and Kosice so it makes a good jumping off point for Slovensky Raj. You can also catch a bus from here to Dedinky, on the south side of the park, though these are not very frequent.
We were lucky when we arrived at the bus station in Spisska Nova Ves as there was a bus leaving straight away for Cingov. The next one didn't leave for 3 hours. It cost only 10 Sk for this journey. In summer (July & August) there are evening buses back from Cingov; at other times of year the last bus leaves at 3.45. We got back to Cingov after our hike, realised it was September 1st and there was no longer an evening bus, so we faced a long hike back to town. Not a nice prospect after having spent a whole day hiking.