Typically the correct withholding will be single with zero allowances. But this is printed on the form if you (or he) follows the instructions. It's unlikely that state rules will be different in this circumstance but you can check your state tax web site to see if they have a separate withholding form and follow the instructions on it.
Remember that income earned from working is always reported on a tax return in the taxpayers own name, it is not added to the parents' tax return even if the parents claim the child as a dependent.
Your son will be able to file using the free version of turbotax online, but it certainly would be an educational experience to download the actual tax forms and have him do it by hand. The forms for a single person with one job and no self-employment or investments will be fairly simple and easy to manage.
