It helps to know that Thai has 9 vowel sounds (so it's easy: English has between 14 and 21 depending on where you are from!) Think of them on a 3x3 grid according to how high the jaw is and how far back in the mouth the tongue goes:
Front Centre Back
อี อื อู High
เอ เอ้ โอ Mid
แอ อา ออ Low
or (British) English equivalents (don't pronounce the Rs) something like:
ee eu oo
eh er oh
air ah or
The 'eu' sound isn't found in English, it's a bit like the German ü-umlaut or the French u in 'tu'
Then each vowel can be short or long, there are diphthongs and a couple of triphthongs, and each syllable can have one of 5 tones: level, low, falling, high or rising. Apart from that it's straightforward ;-)