Hi, I'd like to help you with your question.
You may be able to believe your son, depending on whether or not he has lied to you already in the recent past or if he has been honest for the most part. Also, if he is getting any pressure to quit his drug use he may say he has just to stop feeling the pressure. You may be able to tell if his behavior is different or he is still following the patterns he did before such as hanging out with people who use, not taking care of responsibilities, evasive behavior when asked about his whereabouts, etc. These all indicate he has not changed his behavior. But if he has tried to move out of that lifestyle and has shown you different behavior than before, then most likely he is working on his recovery.
If your son has quit on his own, that is a great first step. However, it is highly unlikely he will stay clean unless he gets help and support. He needs to be seen by his doctor first, to be sure his health is ok. Then he can talk to his doctor for a referral for treatment. A drug and alcohol treatment center or just seeing a therapist for individual therapy is a good way to get started. Cognative behavioral therapy (CBT) is a therapy that can help him learn to change this thinking and therefore his behavior around his drug addiction. Twelve step programs are also great in providing support and sponsors to help him change his life and remove himself from the drug abuse lifestyle he dealt with before.
You and your family can also become involved with your son's recovery. Narcotics Anonymous helps families cope with family members who use. They provide support an resources to help. Here is a link: www.naranon.com/
Talk with your son about the information here and see what he is willing to work on. He may not feel comfortable doing it all, but even a small step towards recovery will help keep him moving forward and not back to the drug use, especially if he feels stressed about measuring up.
Here are some books for you and your son to help:
Willpower's Not Enough: Recovering from Addictions of Every Kind by Arnold M. Washton
12 Stupid Things That Mess Up Recovery: Avoiding Relapse Through Self-Awareness and Right Action by Allen Berger
Enough Already!: A Guide to Recovery from Alcohol and Drug Addiction by Bob Tyler
Everything Changes: Help for Families of Newly Recovering Addicts by Beverly Conyers
You can find these on Amazon.com or your local library may have them for you.
Most of all, be there for your son. Talk with him, encourage him, and be someone he can turn to if he relapses, which is common with addiction. If he knows he has you, he will have a better chance at pulling himself out of the addiction and living a better and more productive life.
I hope this has helped you,