Because I am taking physics, I think this should be some practice that is actually fun.
We need 1.24*10^29 J to break the moon's gravitational binding energy according to one guy on this website: https://worldbuilding.stackexchange.com/questions/8951/how-much-tnt-do-you-need-to-blow-up-the-moon
Because of this, let's just say that we need 1.24*10^29 N of force to destroy the moon, so in the comments, add to the Newtons of force exerted upon the moon (I know just adding all of them up is unrealistic as heck, but that's what I'm doing).
You could try doing things such as rocketing satellites into the moon or just hitting it REALLY HARD with a sledgehammer. However, you can't blow it up using conventional explosives because there is no oxygen in space. To add explosions, one must use C4 or another kind of sealed explosive.
Don't worry about calculations! (You can do them if you want, though. I'm not stopping you.) I can do them for you, delivering approximate results! (Assume impact time of .1s)
Alright, let's get crackin'!
I use compressed air to shoot a sledgehammer (9kg) at the moon really fast (200 m/s)!
Starting force: ~36000N
Current force can break: ~4.5 average femur bones