Short hop laser is pretty simple to start from. Tap your jump button, or flick your control stick. Once you are in the air (you may wish to be ready to press it before Falco is in the air) press B. Falco crouches for a short bit before entering the air. This is known as jump squat, and you must release your jumping input before he finishes crouching to short hop. If you grab, use your up-special, or upsmash while Falco's crouching, he won't jump and will perform any of these moves.
When shooting a laser, you're vulnerable, and there are many frames in the animation where you're not producing a projectile or any kind of hitbox, and in this time, the opponent is free to move. Any time you're letting them do something because you can't do anything to challenge is potentially you being punished. To minimize the time they can do this, you want to minimize your air time, because when Falco hits the ground lasering, it cancels most of the lag normally associated with shooting a laser. When Falco reaches the apex of any of his jumps, or stops rising, you can hit downward on the control stick to fast fall, and lower your landing lag. Ideally, you shouldn't keep holding it down, just tap it.
Lasers are one of the biggest parts of Falco's neutral, or rather, shutting down the opponent's neutral, but what do you do when there isn't room to laser, or you've got in with a laser? They don't deal a lot of damage or stun, they're mostly just disruptive. Well, at this point, most Falcos like coming in with an aerial of some sort. There's a few properties that make people comfortable approaching with them over other moves.
Firstly, aerials can not get out prioritized by ground moves, or other aerials. If you have a good hitbox you're using, it doesn't matter if the opponent's move is stronger, the hitboxes won't interact, you just have to hit them first. Second, it's very easy to control your motion using an aerial, or just move forward attacking in general with one compared to another type of attack, and thanks to this and other things, you can hit with specific hitboxes easier using an aerial. Third, many aerials, such as Falco's dair and nair, have long lasting hitboxes, and generate some amount of threat throughout the move.
At higher levels of play, some of these reasons become a bit less relevant, you ideally want to hit with most aerials as late as possible, when you're landing, for the purposes of this post, mostly. While being in the air with a jump means you can more readily do an aerial or laser to create threat that ignores priority rules* (but not hitbox geometry), or instantly double jump to get out of there, or air dodge to do something like a spotdodge that can last variable amounts of time (or waveland/triangle land), you still can't shield, dash, or use most of your better defensive options. You're almost entirely more vulnerable in the air than on the ground, so you want to spend as little time in the air as possible again.
*Priority rules still apply to aerials vs items and projectiles, assuming none of the moves involved have transcendent priority. Certain moves like Fox and Falco's Illusion/Phantasm, and Sheik's vanish have projectile hitboxes attached, and thus can clank with aerials, though they won't cancel the animations.
Introducing, SHFFL: Short hop fast fall l-cancel. Or in other words, doing aerials more rapidly than ever. As mentioned earlier, you want to hit with aerials low to the ground for the most part, and to minimize air time, fast falling is essential. When doing an aerial, unlike a laser, you hit a shield button (doesn't have to be all the way) or grab button to cut your landing lag in half. You want to do an aerial later for a few reasons. When you do an aerial earlier, you cut off other options you may want to take later in the jump if it becomes apparent you won't hit, like lasering if they're far enough away, or wavelanding back if they're dashdancing to avoid the aerial. Another reason is because you're mostly going to want to hit with the strong, early hits of Falco's aerials; they're better at lower precents and stronger vs. shielding. Finally, when you aerial later, your hit is pretty much guaranteed to land closer to the ground (if it's going to hit), and thanks to L-cancel, this more or less means you can link an aerial into another move faster than largely any other two hits in the game. Important for dealing with lower percents and CC to build percent quickly if you can't get a grab.
Whew, that was a long one! So again, on lasers, you can control your approach and lock the opponent down, but the lasers actually have to be shot at the opponent to fulfill this purpose. You can try pressing the b-button and the fast-fall at different times for different heights, but you need to be facing the correct direction. To reverse laser, simply press the direction you aren't facing, let the stick return to a position where you can laser and not Phantasm, and press B. Pretty simple. You may also wish to turn around if you're offstage facing the wrong way to increase your recovery options, but here, it's probably better to turn around in reflector.
On the topic of Falco's reflector (or shine as it's called) while the move does an okay job at reflecting projectiles (it's got some serious endlag if you do this however), you'll mostly see it used to stall/aid recovery, or to exert pressure or perform combos. Ideally, you want to spend as little time in the reflector as possible. To practice JC shine as quickly as possible, tap jump with the control stick (hit up) or press x or y, or whatever you're most comfortable with after hitting down-b. If you're in it for longer, you need to keep holding B as you jump out. To perform more quickly, you can either just practice shffls on a Ganondorf CPU with handicap 9 while you have 1 (possibly on damage ration 0.5) and just try to speed them up as quickly as possible to simulate hitting players and shields. If you have 20XX, you can also set knockback to zero, or try to do aerial->shine on shield low enough that you prevent a shield grab, and shine->grab or a second shine to ensure you're acting out of shine relatively quickly. Ideally, you should try this vs. someone like Marth so that your spacing or timing has to be somewhat better than it would vs. most other characters.
Dash inputs are the most basic thing and I kind of just assume most people have them down for the most part, so just makes sure you're comfortable Fox trotting without planning to do so in advance (do your initial dash in the same direction twice), learn the farthest distance you can dash before you can't dash back the other way or pivot (input just past neutral the opposite direction and let it return to neutral). The easiet and fastest options to use out of dash are dash attack (situation, never use at 0, only use to interrupt an action or as part of a combo/tech-chase) jumping (and everything you can cancel a jump with), shielding, grabbing and side-special (generally speaking, don't use this onstage). Try to get comfortable moving around, and maximing distance for short hops, and jump-cancelled grabs. Try not wo wavedash so much when the opponent's closer, keep the option open to shield.
If you get past the point where you can dash dance or pivot, you can cancel Falco's full run if you keep holding the movement direction by rotating the control stick down. Try not to go all the way down so that you have the most options out of the crouch. If you weren't holding in the direction of movement as the inital dash is ending, just wait a little and Falco will return to a standing position. Alternatively, wavedash.
DI. To maximize the change in the direction you're getting launched, you want to hold the stick perpendicular to where the move would launch you if you didn't even touch the stick. You don't always want to DI this way however. To avoid combos with DI, you generally want to to have the knockback launch you in whatever way it's hardest for the character to follow up on you. DIing for more horizontal launch can force a tech-chase, but Falco's techroll is hard for most characters to cover if it doesn't start next to them, or go towards them. It's mostly something you'll learn to do with experience.
Survival DI should not always be towards the corner, only when you're actually at risk of dying off the side or top blast zones. Otherwise, going as high as possible is ideal for Falco, generally speaking.
The shield button's pretty important. There's l-cancelling, wavedashing, wavelanding and everything you do out of shield as important things to learn. For out of shield options, you can learn shieldstun by trying to buffer inputs out of shield with the c-stick after someone hits it, which is easy to do with 20XX if you have it. Anything involving jump out of shield, you want to release the shield button as close to when you hit jump as possible. You can do two separate l-cancel inputs to account for whether or not you hit something, but most people don't do this. I most just recommend hitting dummy targets like stand CPUs or 20XX cpus to get basic timings down here, then play matches with your friends and just try to get them consistently (or play like you will get the l-cancel until you're always getting it). Wavedashing, just grind it out, you want to airdodge as close to the ground as possible if you want longer distances, same with waveland. Triangle jumping can potentially be useful, but you shouldn't seek to practice using that first.