Americans and EU Citizens do not need a visa and can stay in Kosovo for an indefinite period of time. Citizens of other countries that have significantly contributed the rebuilding of the Kosovo probably also do not need visas either, although Kosovo is starting to implement a stricter visa regime.
You can enter Kosovo through the northern border with Serbia through North Mitrovica. From Montenegro you can enter by going through Rozhaje to Peja. From Macedonia you can take a bus to Pristina. There is a border entry in the Presheva Valley in Serbia. From Albania you can enter through Prizren.
The are direct flights from Pristina International Airport to London, Zurich, Geneva, Gothenburg, Copenhagen, Vienna, Hamburg, Hanover, Düsseldorf, Berlin, Frankfurt, Munich, Stuttgart, Bremen, Rome, Verona, Ljubljana, Budapest, Tirana, Istanbul and Antalya.
There are direct bus links to most cities in Germany, Switzerland, Belgium, Albania, Bulgaria, Turkey, Macedonia, Bosnia, Montenegro and Serbia.
BUS - is used to travel inside city (you'll be expected to pay 0.40 EUR upon entry), best intercity communication is relying on bus's too.
TAXI - you can use taxi to travel anywhere.