The non-flight option is bus/car & train. You can get a bus or private car from Siem Reap to the border -- your hotel or any travel agent in Siem Reap will easily organize this. Once you cross the border you'll need to get to the train station and get the train to Bangkok. If you book through an agency they may hand you off to someone on the other side of the border who'll help with the rest of the journey. Or I'm sure there'll be people hanging around to help tourists get where they're going (standard warnings about getting scammed apply).
Or you can do it yourself, get to the station and take the train to Bangkok and you should be able to buy tickets on the day, they should understand enough English for you to be able to communicate -- it's a fairly common tourist route. Remember you'll be in Thailand so you'll need Thai money.
I've done it in the other direction as part of a tour and it's a perfectly fine journey, do expect a fair bit of waiting around at the border, in stations etc. Where decent shoes, I remember the border crossing and area around it being fairly dusty/muddy. But it's easily doable in a day if you leave early morning. You'll get to see a fair bit of countryside and you'll be travelling with mostly locals. Note you will probably have to carry your suitcase around when switching between transport and doing the border crossing.
More details and pictures, on seat61.com
Edited to add: This isn't the easiest way, flying is the easiest way. Also check the visa regulations for Thailand, I recall from a different you get less time to stay in the country if you enter via land and you may need to prove you have onward travel from Thailand within that time-limit. See this question for more: Do I need a bus/train/plane ticket out of Thailand in order to get a Visa-on-Arrival?