By air:  Regularly scheduled flights come to Kosice (from Prague, Vienna and sometimes from Brno and Moscow) and Bratislava (from many cities, including Zurich, Prague, Moscow, Tel Aviv and Persian Gulf states).  Other destinations are added from time to time, but these are fairly stable.
Charter flights reach many more regional airports, most notably to Poprad, the gateway to the Tatras mountain ranges.

By train:  Many of Europe’s busiest train routes pass through or very near Slovakia (for example, Vienna’s position 100 km from Bratislava makes connections easy and practical).  It is especially simple to travel from neighbouring countries. There are also regular trains directly to and from key cities in Germany, Italy and Russia.

By bus:  Most countries in Europe are connected with Slovak destinations by regular service, ususally direct.

By car:  Slovakia is now in the process of connecting its key cities by express motorways, but this project will not be complete for many years.  At present, dual carriage motorways are limited to the areas around the larger cities, with the longest section running some 100 km north from Bratislava.  However, smaller roads are generally in good condition.

By boat(!):  Scenic river cruises from Vienna and from Budapest regularly visit Bratislava, making for an especially delightful summer outing.  Overnight stays can be arranged.