If you want to go from Arica to Tacna in Peru the most convenient way is to take a colectivo taxi. We were able to negotiate one from the airport without having to go into town. All you need is four passengers who are wanting to cross over and away you go. It cost us 5000 pesos each for the fare and the taxi driver helped us with all the paperwork through the border.
Our flight from Iquique to Arica arrived late at night and I was wondering about getting into town. Not a problem. Taxi drivers were all over the arrival terminal. Didn't see any shuttles or buses. The ride to our downtown hotel was 5000P/$8US for two of us.
A taxi anywhere in the city was 1000P. The 'yellow taxi' was 700P per person to the Azapa Valle. A half day city tour was 9000P/$15 each. A bit expensive I thought, but worthwhile nonetheless.
Bus ticket (Pullman) from Arica to Iquique was 6000P/$10 each. No frills but comfortable enough.
We were told it is sometimes very hard to get a bus ticket from San Pedro across the Andes to Argentina. We bought ours at the Geminis office at the the bus station in Arica. Cost was 15000P/$25US each for a 12 hour trip (ordeal).
There are about 5 flights a day To Arica, from Santiago Airport, or from Iquique Airport.
The cheapest airfare is about USD120 Roundtrip departing from Santiago.
Buses in Chile are nice, reliable, and comfortable. Arica is a hub for northern Chile. From there you can get tickets to far off destinations in Peru and Bolivia as well as national locations.