Kinesthetic methods of teaching literacy are usually based on phonics, but build tactile and movement exercises into reading instruction.
The idea of a kinesthetic learning style came into the academic sphere in the mid 1900s, and continues to be explored to the present day. Kinesthetic learners absorb information most easily through "doing" rather than "hearing" or "seeing".
Programs that use kinesthetic methods would include:
Tracing letters and words in the air or on paper
Creating words or lettings out of clay or drawing them in the sand
Clapping out syllables
Tapping fingers for different sounds
Moving around different tiles that represent sounds or words
Feeling throat vibrations while saying different sounds
Saying a word then feeling an object that represents that word (say cup then pick up a cup)