Go in training mode as Mario, set the speed to 1/4.
The only things you can do OOS are aerials, specials, and Usmash.
As Mario, shield and unshield while spamming up on your Cstick. You will notice a small delay before Mario begins his Usmash, which is the 7 frames of a shield dropping.
Next, hold shield again. If you have tap jump ON, then do a Usmash while in shield with your control stick. Notice how there is no delay for the shield to drop, the move just activates instantaneously. If you have tap jump OFF, you will need to jump before Usmashing, easily done with a Cstick. So you would shield, jump, and press Up on your Cstick before your character jumps. It is the same thing as doing it with tap jump on. (I personally set jump to one of my triggers so this would be easier, since I play with tap jump off.)
You can do the same thing with specials and aerials, except I think Up B just negates the shield drop lag and does the grounded version of the move, similar to Usmash OOS. The others, like Nair OOS and Side Special OOS are just jumping out of shield and using them in the air, albeit still very good options.
And that's what OOS is. 7 Frames of shield drop lag isn't much, especially in a game that's not as precise and Melee, but I find at high level when you're fighting characters that are fast as hell like Sheik and Pikachu you are going to need everything you have to punish those characters' whiffed attacks.