Ao Nang isn't that big, but while it's nice to stroll about in the evening, by day it's best to save your energy and avoid being fried by the sun. Some islands and beaches cannot be reached by road so other modes of transport step in.
Here are some very Thai ways to travel.
Songtaew Bus (two benches)
If you want to travel longer distances, local taxis or songtaew are converted pickup trucks with 2 benches in the back, covered to protect from the sun, will take you to Krabi town and other beaches.
They're a kind of public transport that goes back and forth between towns. You'll see them driving around beeping their horns, just wave to flag one down and jump on, often you can make friends with the other passengers. Fares are charged per person.
If you want to go island hopping (Koh Poda, Koh Gai, and Ko Tup are just offshore) or find a new exotic beach, take one of the longtail boat taxis from the south end of Ao Nang Beach.
Tickets can be purchased from the booth near the Phra Nang Inn corner of the beach road. Rates are standardized and posted. A one-way seat to nearby beaches is 100 baht per person, while hiring an entire boat for a day of island exploration starts at 2,000 baht. Travel after dark costs more.
Note that, especially on return to Ao Nang, there may be 30 empty boats bobbing idly in the sea, but not one will move until it's financially beneficial; i.e., the boat must be full (the definition of 'full' is influenced by the season, alignment of the stars, and a lot of luck). That means waiting for additional passengers or negotiating a price for a low-occupancy trip - which is basically buying the empty seats.
A samlor is a motorbike fitted with a multi-passenger sidecar which is designed for transporting visitors from one end of the beach to the other.
Samlors and taxis make regular circuits around Ao Nang and you can catch them on any part of the road (or pavement).