What you need to do is contact the local school district, let them know that you feel your child could benefit from speech therapy. They'll include your son in the "Child Find" program and screen him for multiple issues. They cover everything from speech, language, occupational and physical therapy.
They do the initial screenings usually once a month. Then, if your child needs a full evaluation, they'll schedule it. After the evaluation(s), they'll then schedule a meeting with you and the various people who have evalutated your child to come up with IEP (independent education plan).
If your child qualifies in at least two areas, (speech and language each count as one), you'll be able to enroll your son into the preschool for free and they'll drop him off/pick him up for you. Also, it's a federal law that your evaluation and meeting process be completed within 60 days so if they drag their feet, begin making a pain of yourself.
We're going through the same thing with our son. He was evaluated and found to have delayed speech and language skills. Our final meeting to do his IEP is next week. I'm not sure which city you're in, but if you're in the Dysart SD, I can give you some phone numbers of whom to contact. PM me if you'd like them.
~W.