When trying to get SHFFLing down, it's easiest to break it down. First get comfortable short-hopping. Some people use X, others use Y, it doesn't really matter. Just don't use the analog stick, since it'll make things more difficult than they need to be.
Next get comfortable short-hopping and L-cancelling aerials (without fast falling). This will help you get used to the timing that the aerials come out, and what it looks/feels like when they are successfully L-cancelled. Some people use analog direction + A, some use analog direction + Z, and others use the C-stick. Again, it's mostly down to preference, but I find it a lot easier to use the C-stick the majority of the time. It allows me to do things like throw out a knee while going backwards, b-air when going forwards, and SHFFL stomps more consistently. I will say that for instant up-airs/knee/b-air, I use analog + A. You don't have to be tethered to one method. Don't forget to practice L-cancelling aerials from full hop too! On level ground throw out the aerials at different heights; know which aerial's hitboxes can come out when you're only "X" feet from landing. Full hop --> aerial --> L-cancel --> land on platform is also very useful. You'll notice that on some stages Falcon can full hop aerial and land on the top platform, and on others he can't.
Finally, bring it all together into the SHFFL. A common issue is throwing out the aerial too late, or fast falling too quickly. If you find yourself doing either, forget about L-cancelling and just get the timing for the aerials/fast-falling down. Work in the L-cancelling afterwards.
