A reader of an alphabet learns to convert letters into sounds in order and assemble the result. That method fails on Tibetan, and understanding why is most of what separates decoding the script from reading it.
Four things get in the way. The first letter written may be a prefix, contributing no sound. The letter above the root may be a superscript, likewise silent, and both of them may instead be affecting the tone of the whole syllable rather than adding anything of their own. The vowel is written on the root and is then modified by whatever suffix follows, so it cannot be settled until the end of the syllable has been reached. And the tone, which in the modern language carries much of the distinction between words, is a property of the entire stack computed from several of its parts at once.
The consequence is that a Tibetan syllable is read as a unit. An experienced reader takes in the stack, identifies the root letter, and produces a syllable whose sound and pitch follow from the whole arrangement. The tsheg, the small raised dot between syllables, is what makes this possible at speed: it says where one unit ends, so the eye is never in doubt about how much to take in at once.
None of this makes the script irregular. The rules are consistent and there are not many of them. They simply operate on the syllable rather than on the letter.