Nationals of the UK can stay in Slovakia upto 180 days and of USA can stay upto 30 days without a visa.   Canadian citizens and citizens of the EU also do not need visas for stays up to about 90 days. Except nationals of Czech Republic, everybody else needs a visa,   which can be obtained at any of the Slovak embassies abroad. Check with the nearest embassy to confirm whether you need a visa or not.

One thing to note: a legislation has been passed by the authorities, whereby foreigners are required to have US$ 65 for every day they will be spending in the country. If you don’t have this, you need to show a credit card, an invitation from a local resident, or some such document that will prove that you won’t end up being a liability on the government. The law isn’t enforced very strongly, but you are liable to be questioned, so be prepared. Also some nationals need to show proof of medical insurance. For more information you can contact the ministry of foreign affairs.