Get in Koh Phangan
The closest airport is Ko Samui (USM) which has frequent flights from Bangkok and Phuket, daily flights from U-Tapao and Singapore, and several direct flights each week from Chiang Mai and Kuala Lumpur. Transportation to the ferry dock is easy to find at the airport. Ferries depart several times a day with the last one around dusk.
The next nearest airport is Surat Thani (URT) on the mainland. Flights from Bangkok there are significantly cheaper (1,000-1,500 baht in advance, or 2,000-2,500 if booked same day, instead of 3,000-5,000 if flying to Samui), as there are low-cost carriers (AirAsia) flying there, and even Thai Airways charge 30-50% less than to Samui. However, you'll then need combined bus + boat travel to get to Ko Pha Ngan, which will surely take several hours. AirAsia uses the old airport in Bangkok, Don Mueang, while Thai Airways uses the international airport, Suvarnabhumi.
Nok Airways is now selling a combined package ticket including airfare to Surat Thani or Nakhon Si Thammarat, bus ride to the pier, and a ticket on the Lomprayah high-speed catamaran. This should be simpler for travellers than arranging the individual segments separately. Nok uses Don Mueang Airport in Bangkok.
Sunset Baan Tai and seaview to Ko Samui Ko Samui / Thong Sala
From Ko Samui: There are at least 3 ferries a day from Ko Samui's "Big Buddha" pier directly to Haad Rin. Ferries also leave from Nathon and Mae Nam piers to Thong Sala several times a day.
Watch out for scammers at Ko Samui airport who try to sell you a bus/boat combo for an exorbitant price. Make sure to walk towards the exit of the airport where there is an Information counter and taxi stands.
From Ko Tao: there is fast Lomprayah catamaran operating twice a day to Ko Tao for 400 baht at 08:30 and 13:00 or leaving Ko Tao for Ko Pha Ngan at 09:30. The ride between these islands takes 1.25 hours. A cheaper, but slower ferry operates from Ko Pha Ngan to Ko Tao by Songserm express and costs 300 baht, leaving Ko Pha Ngan at 12:30, and takes 2 hours.
From Surat Thani: night ferry leaving at 23:00 from Surat Thani city (walking distance from bus stations Talat Kaset 1 and 2) arrives at Thong Sala pier-Ko Pha Ngan at 06:00 and costs 400 baht for a space on a mattress on the boat. The night ferry leaves from Thong Sala-Ko Pha Ngan for Surat Thani at 22:00 for 400 baht arriving around 05:00-06:00.
By bus and boat
The best way in by bus is by Government Bus to the Na Dan ferry piers: these are the most direct, quickest, reliable, safest, and hassle-free services. Tickets for these services can be bought at Sai Tai Taling Chan (southern) government bus terminal in Bangkok.
Buses also arrive in Surat Thani, capital of Surat Thani Province, . From here you can buy a ticket for a bus + boat ride for the slow ferry (320 baht for the 3 hour ferry and bus ticket to Don Sak) or the fast ferry (400 baht for the 2 hours ferry + transportation to Don Sak pier). both ferries stop at Ko Samui first, and will drop you off at the pier of Thong Sala. Please note that both options will require you to change buses. This should be a quick and easy change over.
If there are no available options listed above (usually only if you've arrived to the bus terminal quite late in the evening before a weekend or holiday), you can also try a bus to Chumphon and board a ferry there, see "By train" below. You can buy a combo ticket on the bus station, it will cost same as if purchased separately (and the bus arrives 2-3 hours before ferry departure, so you shouldn't be late).
Buses originating from Khao San Rd (or other buses operated by travel agencies) are famous for thefts from passenger luggage. Under no circumstances should passengers on Khao San Rd buses leave valuables in bags that will go in the luggage storage areas, even if the bags can be locked. Consider it inevitable that every bag will be opened while the bus is in motion. Bus + boat joint ticket costs at the cheapest Israeli travel agencies at the west end of Khao San Rd (better said Chakrapong Rd) cost only 500-550 baht depending on whether it's before/after Full Moon party and your bargaining skills, so if you are aware of risks using these buses and careful you can really save money instead of taking pricier government bus which does not leave from KSR but requires you to go to a bus terminal.
A very good option, a little pricier, is using the morning bus (06:00) and ferry combination from the Lomprayah company. A reputable company with an office near Khao San Rd and the option to book online through their website. The air-con bus is very new and the connection to the ferry gives the opportunity for a toilet break and to eat something. Leave early in the morning and arrive mid/late afternoon on the island. One way is 1,300 baht. They also have a night bus. web
By train, boat, and bus
An overnight train from Bangkok is an interesting option. Trains arrive in Surat Thani or Chumphon, and from there you can transfer by bus and then boat. Chumphon is the option if you're planning to stop at Ko Tao, but if you're heading straight to Ko Pha Ngan, consider Surat Thani. Both stations are on the southbound Hay Yai line, but arrival times in Chumphon (when using night trains) are annoyingly early in the morning. For example, the (recommended) express train number #85 arrives around 04:00 after which you'll have to wait about 3 hours for the ferry. On the other hand, if you continue down to Surat Thani you can sleep an extra 3-4 hours plus you will arrive in daylight. Considering the waiting time in Chumphon and the longer ferry trip you will eventually get to Ko Pha Ngan at about the same time.
Combined train-bus-boat tickets can be bought direct from the official Advance Booking Counter at Hualamphong station in Bangkok, although if your train is late, and your boat is already gone then you will have to pay extra for the next boat. Thus the joint ticket may not be the best choice.
If e-booking is not available or not suitable to you for some reason, train tickets may be reserved up to 60 days in advance and paid for by email. In reality, the Thai authorities are lax in returning emails and/or will give the runaround, or flat-out refuse to reserve seats for non-Thais during peak travel periods (Dec-Jan and the Songkran holiday in Apr). If your heart is set on going by train, start early, be persistent, and have a backup plan to go by bus or plane.
Upon arrival at the pier or all around island don't forget to pick up a free guide book Phangan.info with a lot of useful information for travellers (ferry timetables, prices of taxi boats, taxi trucks, where to eat, what to do/see, party dates, maps, accommodation and more).