Banda Aceh has an international airport, so the easiest way to get there from almost anywhere is to fly. Within Indonesia, there are several flights a day from Medan as well as a few from Jakarta. You can also reach Banda Aceh from Kuala Lumpur via low cost carrier Air Asia, for from Penang using Firefly. Note that these international flights are not necessarily daily. See the Asia Airports guide to Banda Aceh for more information on the airport.
If you're in Medan, it's also possible to travel to Banda Aceh by bus. The trip take 9 to 13 hours or more, so it's not really the best option.
As you exit the arrivals hall, there will be lots of people offering you taxis into town. There doesn't seem to be an official taxi counter. A private car into town costs about 50,000 Rupiah (3.00 USD). However, it's worth checking with your hotel, as several of them have free airport transfer services. There is also a bus, which will take you from the airport into the city center, near the main mosque, for abotu 15,000 Rupiah (0.90 USD).