Phi Phi is supposed to have no motorised transport, though there are a few motorcycles with sidecars, usually used for goods and construction material transport. Transport on land is by foot or bicycle, but in the populated areas of Ton Sai, nowhere is more than about a ten minutes walk from anywhere else. Longtail boats sail between all beaches. On Phi Phi Don, you can also walk to any beach. From Ton Sai to Long Beach, expect to pay 40 baht/person in the afternoon, at least 80 baht at night. To have a complete boat to yourself, expect to pay at least 100 baht.
Wheelbarrows are used to transport goods, including your luggage if you like. Expect free transport from the pier to your room, but not necessarily in the opposite direction.
The most common ways to get around on Ko Phi Phi are by foot and by longtail. As with most everything in an area like this, the price for longtail boats is a negotiation. Take some foam earplugs for the longtail boat rides. It's a fun ride but the engines are loud and after 45 minutes it can get to you. Negotiating for longtail boats is usually done according to where you want to go and how many hours you want the trip to last. As an example, 1,200 baht for a 6-hour outing to Ko Phi Phi Leh and Ton Sai Bay from the Holiday Inn Resort.