The quickest way was to 'spike' the gun. This would involve takeing a metal spike (sometimes purpose made, other times a field expedient like a bayonet or a large nail) and hammering it into the touch hole of the cannon then breaking it off flush. No touch hole, no way to set off the cannon. Mind you, this didn't necessarily permanently destroy the gun. You could, with time and labor, rebore out the touch hole. Spiking guns was mostly a way to make sure the enemy wasn't going to be using them on you anytime soon. This would be used in situations such as temporarily capturing a field artillery position or in the storming of a redoubt. Any situation where you weren't going to have time to capture the guns, but also wanted to deny them to the enemy.

Similarly, one could also light the gun's carriage and limber on fire. Again, the enemy could eventually get/make new carriages and limbers and remount the guns, but they aren't doing anything with them until they do.

In situations where you had longer access to them, you may very well choose to just take them and use them yourself! Cannons are expensive. However, if say the enemy uses a different size shot than you did and you didn't want the hassle of keeping them specially supplied with ammunition, there are a couple, rather obvious thing one could do. Most expeditiously you could toss them into a nearby ocean/river/lake. Or fill it with some gun powder, stop up the barrel and blow it up. Or depending on the metal, just smash it with a large hammer until it cracks.

Edit:. I remembered another method. Break the trunions off! A cannon without trunions can't be mounted and aimed effectively.

While more can always be said, I covered some methods of spiking cannon and methods of repair here