Qatar Airways, Bangkok Airways, Singapore Airlines, Air Asia are some of the carriers taking you to Cambodia's international airports.
Phnom Penh International Aiport and Seam Reap International Airport of Cambodia receive lots of flights on a regular basis. You can arrive at any of these airports and then take a bus or a share-taxi to Kep. It takes about 3 to 4 hours.
Share taxis are the most popular forms here. They are definitely relatively cheaper. You can hire a private car which would cost you $26 or $32, depending on the vehicle.
Cambodia has revived its old train service. The line runs from Phnom Penh to Sihanoukville and has only two stops. One is Takeo and the other is Kampot. Kep is located close to Kampot, so you can get off at Kampot and then take a tuk-tuk or a share taxi to Kep.
There are plenty of buses that can get you to Kep from the nearby areas and even from the airports. Buses leave from Kampot and Phnom Penh near the central market area. Buses can also get you to Kep from Sihanoukville and Siem Reap.