The closest airport is in Phuket, which is a little more than 1.5 hours away by car, and is serviced by several international carriers as well as low cost Asian carrier, Air Asia.
Ko Kho Khao may be reached either from Takua Pa to the northeast or Khao Lak and Phuket to the south. To get here by bus you'll want to catch the Takua Pa to Phuket (or the other way around if coming from the south) and tell the driver you're going to Ko Kho Khao. They will drop you at the mouth of the road leading into Nam Khem village. It's a solid 5 km hike to the pier from here, but chances are a songthaew will pick you up along the way. Buses to Takua Pa depart from all over south Thailand as well as Bangkok.
If coming from the Takua Pa bus station, a songthaew will charge 200B (they may start with a higher quote but can be bargained down to 200) for a ride to the pier. A motorbike will make the trip for 100B if you're travelling light. If coming from Khao Lak, it's also possible to book mini bus transfers to Ko Kho Khao for 350B all up, or groups could hire a private minivan to Nam Khem pier for 1,800 baht.
When heading back to the mainland, many book taxis that use the car ferry to take travellers all the way to Takua Pa (600B) or Khao Lak (800B). Otherwise, there are generally songthaew taxis waiting on the Nam Khem side of the pier, which will charge around 400B for a lift to the Takua Pa bus station.
Longtail boats ferry passengers and motorbikes to Ko Kho Khao and back all day from 07:30 to around 18:00, although they will run a bit later if there's enough demand. The cost is 20B per person (and 20B for a motorbike if you're bringing one along), and the trip takes just 15 minutes, although you may have to wait for up to 30 minutes at the pier if there aren't enough passengers yet. There's also a car ferry that leaves every half hour and costs 150B per vehicle including fare for the driver.
Once you reach Ko Kho Khao there are usually plenty of pick up truck taxis and even a few tuk tuks ready to take passengers to their resort of choice. The fare shouldn't cost more than 100B to Ko Kho Khao Resort, cheaper for the ones closer to the pier.
Note that during the rainy season months of May-October ferry times and schedules are erratic and weather dependent.
Motorbikes may be rented from several resorts or from a handful of travel companies near the pier for 300B per day. Ko Kho Khao is a great place to explore on motorbike, but you can also take advantage of taxis and tuk tuks for one off trips around the island. Mountain bikes are available for rent from Koh Kho Khao Activity Center (T: (089) 470 0191) for 150B a day. Because of its large size and long roads, Ko Kho Khao is not really conducive for walking, except on the beaches of course.