From Bangkok, take a taxi going to Hua Lamphong Train Station. Be there before 4:30AM to make sure you have enough time to secure a ticket and all that.
Buy a ticket going to Aranyaprathet Station. Train leaves at 5:55AM. Ticket is about USD 2.5 (48 Baht) (6 hrs travel by train).
Get off at Aranyaprathet Station and take Tuktuk to the border (12 minute ride). USD 2.00 (48 Baht).
Upon getting off at the border, Just follow the post/sign or other travelers who are crossing the borders. Thailand Immigration Office (left building). Fill out Thailand Immigration Departure Card and line-up.
Get out of the building and walk to the Cambodian arch. Line-up at Cambodian Immigration office for your passport stamp. Go outside the building and take a Khmer cab (you can talk to other travelers to split fare with, at least 4 passengers) going to Siem Reap. ( USD 15 each).