It is a lunisolar calendar, which has the beginning of the months at new moon. The months are alternating 29 and 30 days long, except the 7th month which changes length. About every third year the 8th month is duplicated to keep the lunar calendar in track with the sun.
However of the four possible year length in this scheme only three occur, a year with both leap month and leap day is not allowed:
The months were simply named by counting them, the first month starts in end of November/start of December. Two other month numbering schemes were used by the northern kingdoms of Lannathai, making a month n of Lannathai to be n-2 in the central Sukhothai kingdom, and n-1 in the Shan kingdom of Keng Tung.
Every month is divided into two parts, the rising of the moon (บึ้น = kuun) till full moon which is always 15 days long, and the falling (แรม = ram) till the next new Moon. The 8th, 15th, 23th and last day of the lunar month are called Wan Phra and are the holy days of Buddhists. The 15th day marks the full moon and is called Wan Phen, the last day marks the new moon and is called Wan Dub. All other days are just numbered.
The neighboring countries of Laos, Cambodia and Myanmar (Burma) have very similar traditional calendars. The main difference between the cambodian and thai calendar is the fact that the lunar months have names in Cambodia, while in Thailand they have just numbers. The traditional Burmese calendar is a bit more different, instead of the three year lengths noted above years with 354, 384 and 385 days are used, and thus a different intercalation scheme.