The nearest airports are Krabi Airport, Trang Airport and Phuket International Airport. Krabi and Trang are both domestic options, they have direct road and boat connections to Ko Lanta, they are also the cheapest/best options if you're only visiting Ko Lanta.
Nok Air offers three-daily flight+ferry services from Bangkok to Ko Lanta v.v. by flying with Nok Air from Trang and transferred on a ferry to Ko Phi Phi. This can be booked directly from their website.
Air Asia offers three-daily flight+ferry services from Bangkok to Ko Lanta v.v. by flying with Air Asia from Krabi. This can be booked directly from their website.
Air Asia runs a free transfer van from Krabi Airport to Ao Nang Pier where you can catch the 10:30 am Ferry. However the Ferry only runs November to April, and might not be running if the weather is bad. The express transfer (see next) is a better option in case.
The quickest service from Krabi Airport and Phuket Airport to Ko Lanta is by using the express transfer which is a combination of minivan and speedboat travel. If you arrive early you will not have to wait for the ferry and if you arrive late at these airports you can still arrive on Ko Lanta the same day.
From Krabi airport a 45 minute air conditioned minivan to the first car ferry port. You then go on board the speedboat which then takes you on a stunning boat ride across the water along the coastline of Ko Lanta. The journey takes around 15 minutes depending on weather and conditions. You will arrive directly in Saladan (alternately written as Sala Dan) on Ko Lanta, where you are then transferred to your hotel by car. That means the total journey time should be 1.5 to 2 hours. This eliminates the waiting time at the car ferry and also if you are going from Ko Lanta to one of these airports allows you more time to enjoy your visit.
Ko Lanta does not have roads connecting it directly to the mainland, but is served by car ferries. Take Rt 4206 off Hwy 4 about 20 km southeast of Krabi airport. Drive to the end of the road, where there is a car ferry from Baan Hua Hin to Ko Lanta Noi. From the pier here, turn right and follow the "ferry" signs to the second car ferry to Ko Lanta Yai. Ferries operate 7 am to 10 pm.There are plenty of car taxi and minivan taxi services from Krabi and the nearby airport. These minivans usually don't have much room for luggage (although they can usually find room for one or two large suitcases together with backpacks for the rest of the passengers) so if you're not traveling light you might need to get a private taxi.
When travelling to/from Ko Lanta in the afternoon by road, allow 2–3 hours for the journey as the queues for the vehicle ferries can be lengthy. The passenger ferry which leaves Ko Lanta pier (high season) at 8 am and arrives at Krabi pier at 10 am is quicker.
Private companies on Ko Lanta operate boat services to all popular destinations.
Ferry services run from Krabi, Ao Nang and from Phuket via Ko Phi Phi to Ko Lanta Yai's Saladan pier. During high season, there are sometimes direct ferries as well. Ferry services are subject to weather and to demand. Many ferries have limited room for luggage. Often the ferries dock alongside each other, meaning that to get on and off passengers must clamber onto and across other boats with their luggage. However many times boat staff will be there to help you board your bags.
Ferries depart from Ko Phi Phi at 11:30 am and 2 pm, and take 1 hour. If travelling from Phuket in a single day, you will need to leave Phuket on the 8 am ferry to transfer to the 11:30 am ferry.
Once you arrive, if you have a booking at a hotel/resort, there should be a person at the ferry exit with a sign giving the name of the hotel you have booked.
By passenger van
All the travel agents in Krabi can arrange passenger vans to Ko Lanta. There is no regular, scheduled van service from Krabi Airport, only taxi options. These can be arranged either on spot for an unknown price or pre-arranged via various websites.
There are mini van services running between Krabi and Ko Lanta.
If you want to return to Krabi by van rather than by ferry, ask at your hotel/resort and they will book you on the minibus which will take you there (as a group with others from other hotels), for a reasonable price.
The nearest train station to Ko Lanta is in Trang province just south of Krabi. From there, there are trains to and from Bangkok.