When your muscles are sore from exercising the next day, are you supposed to relax or keep the muscles active?

You can exercise, but don't do anything that focuses on those sore muscles. Some cardio or stretching/yoga. If you want to take the day off of exercise, that's fine, but you can also do workouts that don't focus on working those muscles intensely again.

Hydrate real well, and do dynamic stretches to help with the soreness. Also, some epsom salts in your bath may help.

Active rest, which means stretching and light movements to help your body relieve the soreness...

Stretch, and or lighter work sets of the exercises done the previous day.

I heard you should alternate exercise between the body. Like one day do arm and the other day do leg

Keep them moving, but nothing strenuous.