it's a letter replacement puzzle, basically- x symbol = y letter etc, so if you look at a word and go "well the missing letter there is obviously a" then the symbol in the corresponding cypher word is the one for 'a' through the entire thing.
For example, first word is
Only one missing letter, and the word is "this" (only so many things it could be with the three letters that it already has)
The cypher symbol version of the word is
So the symbol for the missing letter, 'h' is
and then you just go through the puzzle and finding all the cross-with-circles-on-the-arms and going 'that's an H and that's an H and this is an H'
Repeat until complete
(and if you'd prefer to just cheat or get really stuck then you can look at
Amarok's walkthrough for some spoilers)
