The main transport in Phan Thiet is the motorcycle. Most resorts offer motorcycles for rent at about 10 USD per day. Along Mui Ne there are a few makeshift shacks with bikes lined up. Some can be a little dodgy so make sure the vehicle is safe and thoroughly checked for scratches before renting to avoid any misunderstandings. A photocopy of your passport is often required for security.
Be really careful on the road, the left hand driving in Phan Thiet takes getting used to for some and as for overtaking, it can happen anytime and anywhere. Use of the horn is constant and the general rule of thumb is, if it is bigger than you, get out of the way. As such the bigger trucks and tour buses rule the road. If you cannot ride a bike, there are motor-taxis that can zip you around but this is recommended only for short trips.
The traditional cyclos are widely used in Phan Thiet. These are sort of a bicycle driven trishaws with the rider behind and a fairly spacious seat compartment in front. It is no chariot but for the same price as a motorcycle rental, you get chauffeured around at a nice leisurely pace - a good way to take in the sights and sounds.
Taxis are available but can get expensive. Car rentals come with a driver for about 50 USD a day. Renting a car without a driver is unheard of.
From Ho Chi Minh, it takes about 3 hours by car and a little longer with the big coach buses to get to Phan Thiet. Alternatively the hotels in Phan Thiet can arrange car transfer for about 60-70 USD per way.