The only way to land on Kauai for most people is at Lihue Airport, which is located about 2 miles east of the town of Lihue.
Its airport designate is LIH, so when you are booking your flight, search for rates to get you to Lihue. Most likely, you will be connected via Hawaiian or Aloha Airlines, but there are also some direct flights on American and others.
By Air: United & American both have non-stop flights directly to Lihue, Kauai. Flights with Hawaiian, Alaska, ATA & Aloha require a connection in Honolulu.
By Car: A car is necessary to get around this island. Poipu Beach is 16 miles from the airport and generally under a 30 minute drive. Roads are one lane each direction so at times can back up especially if there is road construction.