Situated on the outskirts of Sofia in the direction of Plovdiv, Sofia airport has two separate terminals. Terminal 1 (the 'old' terminal) is currently undergoing renovation and will ultimately be repurposed. For now only a few low cost flights continue to operate from here. Eventually a 3rd terminal is envisaged, but for the time being most flights are operating out of the newer Terminal 2, which under the new management company is receiving a major upgrade. It has become noticably more comfortable and attractive in the departure zones with a good selection of shops and cafes, although all overpriced. In arrivals there is a small duty free shop which is quite reasonably priced and will save you schlepping your litre of vodka around.
There is a multi-storey car park at Terminal 2 with over 800 spaces  which is also undergoing repairs at the moment. If you are based in Sofia and just flying out for a few days, there are several Park & fly type services near to the airport. Worth checking out.
There is also a lovely park area with lake adjacent to the airport, a great place to do a bit of plane spotting and this is also proving a popular event venue.
Getting to town:
The journey into town takes around 30 minutes and by taxi should cost no more that  20 leva for a city centre location. Sadly there are still regular reports of people being ripped off by the taxis hanging around the airport. PLEASE BE SURE to go to official  taxi rank rather than going off with one of the taxi drivers offering their services as you come out of Arrivals. As of 1st July 'Yellow!' Taxi will be the licensed operator for Sofia Airport.
If you can, get someone to meet you at the airport. Most hotels operate a pick up service on request.
For those on a budget there are several public transport options.
There is a metro (underground) stop at Terminal 2 that will take you to the city centre in about 20 minutes. From there you can change to another line depending on where you need to get to. Bus No. 84  travels down bul.Tsarigradsko Shosse via the University to ul. Gurko in Sofia city centre and vice versa.