Our 3 children each had/have speech difficulties, whether it be delay and/or articluation. First and foremost, please realize (perhaps you already have) that all children need a "tweak or two" in there development in order to allow them to grow into all that each can be. It is just our task to help them with these issues!
For our children, we opted to utilize "Infants and Toddlers" before they were three and then "Child Find" afterwards. Depending on where you live, City or County, will determine what program(s) you are qualified to receive. These are state run and are FREE. As tax payers, we help support and fund these programs so it only makes prudent sense to utilize them. And once tested, the program is required to offer services to your child if deemed necessary - not place him on a wait list. There are set guidelines and timeframes when services MUST begin. I will say that you are your child's best advocate and as such navigating through the system is sometimes daunting and frustrating. Just please keep pushing forward.
Also, the public school system in your area is probably the "go-to" at your son's age for speech/language services once he has matriculated into the above Child Find Program. If your son in also enrolled in the school, the therapist and administration will find the best time during his school day to offer therapy. Hopefully this makes it convenient for you and your son.
I will be happy to discuss this with you on the phone if you wish. Please let me know if I should forward my phone number.
For our eldest, we had a wonderful private therapist come into the house. She was a newly graduated Speech/Language Therapist who came to our home. She tutored my daughter, as well as another school-mate of our daughter's, weekly for 8 months. We paid $35/30 minutes. Both girls thrived!
I do not know where you reside. Here in Baltimore Loyola College offers speech/language therapies. There prices are discounted somewhat as graduate students tutor the children, obviously under direct supervision from the professor's and advisor's.
Some of the at-home exercises we do include: blowing bubbles, eating chocolate pudding through a straw (no joke - as this helps them strengthen mouth muscles and practice lip and tongue control and you would not believe how great this works), going through flash cards, playing games and having the kids just ask for what they want, not point. Having your son have to use words to express his feelings and desires will also help. So often, we know what our kids want and will just give it to them, without having to ask. I know that I am guilty of this, as with three children sometimes we are so hurried, I just forget to slow down long enough to practice what I preach.
Good Luck. Keep asking for help. Again, I will be happy to discuss this further with you.