Border posts between Slovakia and fellow EU Schengen member states – Czech Republic, Hungary, Poland and Austria – are almost nonexistent. It's convenient to come in by road, but drivers must buy a vignette, a toll sticker granting access to Slovak highways, at the border (https://eznamka.sk). Checks at the Ukrainian border are more strident, as you will be entering the EU (expect your vehicle to be searched). By bus or car, plan for one to two hours' wait.
Local buses connect Poprad and Ždiar with Poland during the summer season. Eurolines and Košice-based Eurobus handle international routes across Europe from Bratislava and eastbound routes from Košice into Ukraine.
Driving into Slovakia, you'll find fuel and highway vignettes (toll stickers for Slovak highways) readily available to buy near the borders (€10 for 10 days). Non-EU drivers should come armed with an International Driving Permit. Be warned that foreign-registered cars can attract the wrong kind of attention, both from over-zealous police and from scammers. Right-hand-drive cars from the UK will require headlight-beam deflectors.
Private-vehicle requirements for driving in Slovakia are vehicle-registration papers, proof of third-party liability insurance and a nationality sticker. Vehicles must carry a first-aid kit, reflective jacket and warning triangle, and a vignette for highways.
Direct trains operate between Bratislava and Budapest (2¾ hours), Prague (from four hours) and Vienna (from one hour). From Košice, trains travel across the border with Hungary to Budapest (four hours) via Miskolc. Čierna nad Tisou has rail links to/from Ukraine.