The procedures concerning third country nationals entering Slovakia and the EU are in general more demanding than those concerning EU citizens.
The best starting point for the specific information in your particular case is the Slovak embassy in your country.
To get the picture about the procedures when entering Slovakia and to be ready even before contacting the embassy, you can check following sections:
Do you need a document to be apostilled or superlegalised? Find out what it means and what you are supposed to do: Authentication and translation of documents
Do you intend to work in Slovakia? Find more information on Slovak conditions of employment in the category: Employment