I don't really pop balloons, but I have popped a few inflatables before, and I can say that my choice method of popping in bouncing on them. Sometimes they won't pop for a while and you'll need to reinflate them some, but that just makes it so the fun can on longer.
Beachballs are usually easier to pop than ride-ons, so blow or pump them up nice and tight, and they'll usually pop after a few good hard bounces. Ride-ons are more durable, so even when you over inflate them, they may take a while to pop. Now, I'm really not much of a popper, but even I get the urge once in a while, and the harder to pop the inflatable is, the more fun it is for me.