keep exercising even when muscles are still sore
 

Should i keep doing push-ups today even though my muscles are still sore from yesterday or should i give myself a break ?

The rule is to give a muscle group a minimum of 48 hours of rest between workouts. So if you did pushups yesterday, you would want to wait at least 48 hours until you do them again. In the meantime, you can work other muscle groups or do cardio, take a yoga class etc, so you still can stay active. :)