i could probably show you more easily than explain, on keyboard, you can short hop, wait for the right frame window then press up and a without it doing a second jump (all this without buffering up). if instead you do buffer up, you can press a the moment you jump and the attack comes closer to the jump. what i mean is that the window to press up again occurs after a normal uair would begin.
...Why does the attack come closer to the jump, just because you buffered up? You're pressing up DURING THE JUMPING ANIMATION in which you wouldn't be able to press A anyways, so it comes out just as fast. That's why you don't double jump, you're in the jumping animation and any inputs cannot make your character do anything during this short time. The only drawback is it can be a little hard to time with characters with quicker jumps like Pika and Fox.
For platform drop upairs, as well as fastfall upairs retaining your second jump, you have to press DOWN, UP, AND A WITH NO SPACE IN BETWEEN THEM. The timing in between each press is similar to the timing in between C and the first B for Fox's double lasers. If you want to delay the upair in the fastfall upair method, you have to press down, let go, then do the method above. I know all this sounds difficult, but it's really not all once you get used to it. I can do them pretty much 100% consistently.
You can also do upairs without wasting your double jump, and dairs without fastfalling even when you aren't rising from your jump, if you aren't already holding the direction. Both are done the same way, pressing down/up and A at the EXACT SAME TIME. It's pretty difficult IMO and I wouldn't recommend it unless you're in a situation you REALLY need it, but having more options available is always a good thing.