Arrival in Uganda is a nice experience after a long flight. With very modern facilities and friendly staff you will be through customs and immigration very quickly. Have a 50US$ note in hand will make it even easier to buy your visa. You will then proceed through a modern airport and pick up baggage like any other airport in the world.
If you have booked a driver he (and it almost always is a male) will be waiting in arrivals for you with a huge smile and name card. If you need to change money- the rates are not so bad at the airport- he will assist you in doing so prior to loading your bags into the car and driving you to your hotel.
It is definitely not advisable to arrive in Entebbe airport without pre-arranged transport. There are a number of „travel consultants‟ waiting for you and will happily assist you for a nice big fee. Entebbe is also around 40km from Kampala with no public transport options. A Boda Boda (see Staying safe in Uganda section) may get you to Entebbe town and you may make it in on a Matatu into Kampala. A really horrible introduction to Uganda after a day flying!!!