Taiwan's currency is the Taiwan Dollar (NT$ or TWD). The exchange rate varies around 30.60 NT$ to $1 (USD). For more information, this website provides an exchange rate table: http://www.x-rates.com/table/?from=TWD or http://www.oanda.com/currency/converter/
Kaohsiung by plane
Kaohsiung has an international airport (KHH). Kaohsiung International Airport (IATA: KHH) is about twenty minutes to the south of the city center. In 1997 a new terminal was added dedicated to international connections and transfers to Taipei (Taoyuan) international airport. International flights from Asia arrive daily, but unfortunately, there are no direct flight connections between Taipei and Kaohsiung. However, after an international arrival, they can take a local flight from Kaohsiung to Taipei. The airport is on the MRT Red Line and is also easily accessible by scooter, car or taxi.
Some flights to Taiwan from overseas will arrive in Taipei. Then you need to take a speed train. Taiwan High Speed Rail line (HSR). Traveling by train is a viable option for getting to Kaohsiung, as the fastest trains from Taipei cover the distance in just 96 minutes. There are 3 types of tickets: Business Reserved, General Reserved, and Non-Reserved. Reserved are approx. NT$1500 ($50 USD) and non-reserved slightly cheaper at NT$1400. Remember to get Designated Seats if you are traveling with luggage, it's NT$100 more expensive. Buses run the length of the island, with stops in major towns. They feature fully reclining seats, baggage transportation and, on some, video game consoles or televisions for each seat. Prices run around NT$800 per trip, give or take, depending on the initial and final destination. Most major bus companies have their office and stops close to the train station. They are located on the same road as the train station, about half a block down the street.
Kaohsiung by metro
The Kaohsiung MRT opened in 2008, with two lines. The Red Line runs from north to south, offering a handy route from both the THSR Zuoying station and the airport into the downtown core, while the Orange Line runs across the city from the Port of Kaohsiung in the west to the eastern suburb of Daliao. The Metro Line is very clean and offers a convenient way to quickly move within the city. Operation of the MRT stops at about 11:30 p.m. for the orange line and as late as 12:30 for the red line. Ask at the information desk to be sure.
By taxi
Taxis are also available from the airport. The cost of a taxi will probably be around 350 NT$ each way from the airport to the hotel. The city government has established Taxi English Service to allow travelers to search for English-speaking taxi drivers in chosen areas. Taxis can be an easy way to get to some places unfamiliar, and are fairly common in the city. If you have the business card of a location, or the Chinese characters written down, they can easily get you there far faster than most other means. You may ask for the price in advance but as with any other places in Taiwan the meter is almost always used. For more information on what to visit, where to eat and safety measures, see: http://tourism.kcg.gov.tw/en/default1.asp
and http://eng.taiwan.net.tw/
