First and foremost, let's start with the basics, here are the phonemes translated into our alphabet:
(note the missing rings on v/w and jh and zh).
The writing system borrows heavily from Hebrew, with vowels appearing below consonants. Unlike Hebrew this still reads left to right. Also unlike Hebrew (and like English) consonants can be combined the form new consonant sounds (s+h making a 'sh' sound instead of needing a separate letter for example).
The symbols are far more complicated than most writing systems. The system was invented and mostly used by an aristocratic priest class in the beginning. As such, they wanted a system that seemed regal, and was less accessible to the uneducated masses. Eventually, a less stylistic "cursive" was invented, and is what is used when most people write, though books are still published in this classic style.
Want to see what a word would look like in this alphabet?
Check it out.Phonemes grabbed from:
http://www.speech.cs.cmu.edu/cgi-bin/cmudict