There are not fligths from Peru to Arica, peruvian fligths end or start from Tacna and you must go there by land (60 km aprox).
There are not railroad passenger service between Arica-La Paz since almost 10 years ago, you must go there by bus or car..
Arriving by air :
Chacalluta Airport is one of the smallest of the country, but this year will be rebuild by private concesionary to make it bigger and more expensive. It is located just near the frontier border line with Peru along Las Machas beach. At arriving traveller can see clearly the borderline between Chile and Perú, so as the mining camp between the countries. It can be seen also clearly the city layout with two valleys who reach the sea from the high plateau and the green spots in the middle of desert created by Lluta River and San José river, the last almost never reach the sea, because the waters are used for farms of Valle de Azapa .
Custom tramitation for aliens are simple and fast, the good faith presuntion is applied because import taxes are amng the lowest in the world (4% average). You can not miss at airport because its small size, there are just one dissembark gate with a dozen of taxi drivers offering "taxi" (exclusive car) or "colectivo" (shared taxi). The golden rule for a tourist in Arica is always ask for the final price before to contract any service . Following this rule will save you lots of money and bad experiences, remember always this during your stay in the city. Taxis are more expensive than colectives but they are paid in a point of destination basis, colectivos prices are pais in per passenger basis, so sometimes for groups of 3-4 person going to the same point taxi may be more convenient, otherwise we recomend colectivos, in both cases you must negotiate the price in advance.
From airport to the city there are some 15 minutes by car from the north side, it crosses the poor neighborhoods however is a clea and ordered road along the sea and desert. Before to reach downtown the road pass in front of Costanera Sur and Chinchorro Beach , one of the 3 main coast places.
Arriving by land from south
From south of Chile you arrive Arica after to cross Desierto de Atacama the driest place in the world, the trip from Santiago is 2.070 km away almost 30 hours by bus croosing the Valle Central, norte chico (Coquimbo, La Serena, Vallenar and Copiapó), then to the long desierto of Norte Grande trough many hours until Antofagasta, Tocopilla, Iquique and Arica . It is a long and boring trip so we reccomend to take a bus "salón cama" (there are regular buses normales, semi cama and salón cama). Bus fares are often negotiables, you must always ask in counter if there are some special discount or cut price. By plane the trip Santiago-Arica last about 4 hours, by landas we said before thereare about 30 hours.
The road enters by south acces and the first seeing is the Acha jail, then Terminal Agropecuario (food and vegetable market, very interesting) and finally trough Avenida Diego Portales arrives to Terminal Rodoviario . If you has never been in the city before the best choice to move is "radiotaxi", besides Terminal Rodoviario there are the cheapest radiotaxis más baratos (750 chilean pesos downtown, 1500 to the beach and suburbs), there are also a lot of taxi chauferrs offering at the exit of Terminal but they are more expensive, never forget to negotiate price before to take the service.