Entebbe Airport is the only international airport in Uganda and so, unless travelling in by road, will probably be your access point. Opened in 1952, it is probably best known for the scene of a hostage rescue operation by the Israelis after an Arab-German hijacking of Air France airplane in 1976. From the summer of 2016 it is now a requirement that visitors arriving in Uganda have a visa before arrival.
These can be applied for online at https://visas.immigration.go.ug/. The process is fairly simple but remember to upload a copy of your ticket with both arrival and departure dates and preferably an itinerary. The process takes just a few days but apply early in case the application is deferred pending clarifications of your travel.