It must be exciting to see the interest your son has in learning to read and write. What a blessing!
I read that you just received the book, The Writing Road to Reading. I suggest turning to page 9 and reading the paragraph about phonemic awareness. This paragraph suggests several activities for you to try. I am assuming that you are reading to your son already, and that is probably one reason that he is showing so much interest in the written language.
Although most three year olds do not have the fine motor skills to write acceptably on paper, some do. If your son does have the skills and he wants to, encourage him to develop his skills. If not in the confines of lines, practically all children can write in the air, in sand, in shaving cream, and (my personal favorite) chocolate pudding. So, if he writes on paper or in the sand (for example), try to follow the procedures for handwriting as described on page 19 and after. It would also be beneficial to read "Prewriting" on page 10.
You can also teach your son the phonograms with the handwriting. See page 10 about phonograms. It's amazing how well some little children can learn the phonograms when we adults may have a bit of a struggle. If you didn't purchase them, I suggest acquiring the small size phonograms from Spalding Education International.
Finally, you may want to look over the first grade lesson plans on this Spalding website. You will get some ideas of what you can do to enhance his development. These particular plans describe plans for beginning readers but could be adapted for a younger child if used at a slower pace.
Please write back if you would like any idea clarified or explained further.
David, Executive Spalding Trainer