This is a tough one, high school doesn't really offer particular classes to teach or reinforce phonemic awareness even though it is known that it is the leading cause of children reading poorly when entering high school. It just doesn't seem to covered very well in elementary school (where it should be). I have included a few sites that you may find helpful to work on at home, some seem a bit childish, but it does cover the material and sometimes we have to go backwards to go forwards. Give these sites a chance and best wishes!
Mooncat, great question! I've taught syllabification to high schoolers because they need it -- and since their verbal vocabulary development is much higher than say a 1st grader, they can decode a complex word, recognize its sound patterns (and already have an understanding of context), and develop a quick sense of awareness.
I also think poetry is a great way to develop phonemic awareness. In reading it, and then to write it. You can go with the traditional styles which pay particular attention to sounds and syllables, and then graduate to free verse, where a student can explore and test what they've learned.
And for less structured educational time, Hangman is a great game to play that teaches word attack and how to recognize patterns. I have to credit my adjudicated youth students for this suggestion because they loved Hangman; I would run tournaments in class to study key vocab (and give extra credit if they could use the words correctly in sentences).