For a few years, there are direct buses to Cambodia from Bangkok Nothern Bus Terminal (Mo Chit). You are supported from A to Z and just have to do cros the border and get your visa by yourself and then climb back in the bus to continue your journey to Siem Reap, the nearest city of Angkor or Phnom Penh, capital of Cambodia.
The quickest way to go to Cambodia from Thailand is by taking the plane. Whether your destination is Siem Reap or Phnom Penh, the flight lasts about an hour. You have the choice between several airlines. The cheapest tickets are generally offered by Thai Air Asia and Thai Smile.
One of the most taken routes to get to Cambodia from Thailand is the one that goes to Trat in the East of Thailand. In Trat city, you will easily find agencies to sell you trips up to Sihanoukville, Phnom Penh or other destinations in Cambodia. The trip will be in stages: first a minivan will taks you to the border, you will get a visa (think of having a photo ID) and then you will have to share a taxi with other travelers to reach the part of the Cambodian island of Koh Kong, where a bus will take you for the rest of your trip.