If you suspect a LD, a neuropsychological evaluation conducted by a pediatric, developmental neuropsychologist. The professional will assess various aspects of cognition, memory and academic performance to make a diagnosis and recommendations.
Here is an excellent resource about neuropsychological testing.
http://www.drmoldover.com/Child%20Assessment%20and%20Diagnosis.pdfYou could also make a referral to your public school. However, sometimes they do not identify kids that are 2-E, and minimize their struggles - especially if the student has been able to compensate.
You ask what the treatment would be - it would depend upon the cause of the comprehension issues. Sometimes poor comprehension is a result of poor decoding and fluency (but this does not sound like your son's case). Sometimes it is related to attention issues. Sometimes the student has language processing or memory issues. Depending upon the root cause, there would most likely be some explicit instruction that would teach the child strategies to overcome their weakness. If attention is an issue, medication or behavioral interventions may help. The treatment would be designed for the child's specific deficit and age. The evaluator should be able to help you with this.
