Krabi Airport is small and compact, and about 20 minutes drive from Krabi Town. Make sure to bring adequate cash in Thai baht for transportation. Taxis charge a fixed price of 600 baht for a car to Ao Nang that supposedly only has room for three people. You can get a van with more capacity for 1000 baht. It may be worthwhile to share a vehicle with some fellow passengers from your flight.

Airport buses run to Krabi Town (90 Baht per person) and Ao Nang Beach (150 Baht per person). You will see the airport bus desk as you exit Arrivals. The buses wait in the parking lot and do not depart until they're full or there are no more arriving passengers left.

http://www.krabishuttle.com/ - You can pre-book a Private Car, Luxury SUV, Standard Minibus or Family Minibus (a bit larger). The driver will be holding your name on a board as you exit arrivals. Prices are slightly cheaper than taking an airport taxi on arrival. Example: Aonang - 600 Baht for a private car or 750 Baht for a Minibus

Krabi airport pick-up service offers private transfers starting at 580-1200 baht.  

For those on a tight budget, walk out of the airport terminal building, cross the parking lot and then the main road and flag down the next "songthaew" (local transportation - a converted taxi-pick-up truck) heading to Talad Khao Bus Station and/or Krabi Town. From there, you can take another songthaew to the beaches (Ao Nang 50 Baht, Klong Muang 70 Baht).