S.O.
M. ~ You've gotten some great advice so far, but as the mother of my own "active" 3 year old, I thought I'd put in my two cents!
We originally had to put locks on our older two children's rooms to keep him out while they're in school, but - now - we've been able to implement some methods that have successfully reduced our son's destruction.
First ~ our son plays w/playdough daily (he prefers the homemade - recipes online) ... having something to sculpt & squash & resculpt seems to calm him.
Second ~ we try to let him play w/bubbles when it's pretty outside ... he uses his legs to run after the bubbles, his lips to blow the bubbles & his hands to pop the bubbles.
Third ~ we threw out all of the toys he's broken or books he's ripped ... that way, he (A) sees there are consequences for his destruction & (B) has fewer toys in his room to avoid overstimulation.
Fourth ~ we provided him w/toys with which he can build & destroy repeatedly ... he loves building towers w/his legos & knocking them down ... & he enjoys playing w/his magnetix (he can put them together & flip them so the magnets repel)
Fifth ~ whenever I bake cookies or biscuits or pizza dough, I let him help me. He loves kneading the dough w/his hands & thrives on the one-on-one time w/Mommy.
Sixth ~ my husband has him "help" w/chores around the house ... handing him tools, holding the tape measure, etc ... he feels so "big" & enjoys time w/Daddy.
Seventh ~ he enjoys fingerpainting ... we use the Crayola Magic that doesn't stain anything ... can be costly, but for us has been worth it!
Eighth ~ child scissors ... he LOVES cutting up old magazines, old coloring books, etc ... I keep them put up & he has to ask first, but cutting the stuff seems to alleviate his need to destroy AND it's good for hand-eye coordination!
These are a few of the things we've tried successfully.
The key is to provide him w/plenty to do to keep his HANDS busy. His destruction may be boredom, a cry for attention or frustration from overstimulation of too many toys in his room ... it's just up to you to observe your child & decide what's really going on!
BEST OF LUCK!!! Once you find what he enjoys, he'll be like a different little boy!