Why do my muscles hurt the day after working with my trainer & how can I ease the pain?

Muscle Soreness. This is known as delayed onset muscle soreness (doms) and is thought to be caused by small tears in the muscles that occur during exercise. Stretching may help ease the pain, and continuing to exercise will also decrease the soreness as your body becomes more accustomed to intense physical activity.
I agree. Also ice the areas that are most sore to help decrease discomfort. If the pain is sharp and stabbing and does not go away within a few days let your trainer know.