Brief guide!
Quick tip--try your best to fish for grabs. If you can get a down throw on the opponent at low percents, you can either (depending upon fall speed): run forward dash attack, run forward short hop nair, run forward short hop fair, or run forward RAR bair, though the timing is quick on the last one. (Sometimes perfect pivot reverse uptilt works as well, but not always.) All but bair (and pp uptilt) combo into another move if you're quick enough, which can be used to chain nairs or fairs all the way across the stage. If you're at higher percents near the ledge, and you expect your opponent to airdodge, you can do a delayed run forward RAR bair as a read that will likely net you the kill if done correctly. Also from downthrow, you can go for a considerable amount of mix ups, such as "down throw, run forward, bait out airdodge, jab, down throw, etc.," "down throw to short hop laser" to gimp jumps, which can lead to a dair kill at the edge, "down throw, run forward, bait out airdodge, jab, up Smash" which works as a fantastic kill option if the opponent is at high percents and is attempting to do anything other than shield after the jab. Basically, down throw is your friend.
Do not approach with nair, it will get shield grabbed. Down tilt is safer, but don't be predictable. Most people don't respond correctly to Falco's lasers, and if you have conditioned them to shield, free dash grab for you. However, spacing out and fading back and forth is Falco's primary means of approach. (To be specific, Falco likes to do tons of empty hops and tomahawks. If someone jumps at you and you are already in the air, if they haven't begun an attack, challenge them with fair or nair, which will also beat out airdodges. If you're on the ground, and they're directly above you and closing in, up tilt is a good multi hit move to use. Only use upsmadh if they're at high percents and you think you can net the kill.)
LAZY EDIT: you can space bair on shields, without fear of getting grabbed by anyone without a tether grab (or DK), if you do a rising full hop bair. For characters with bad grabs, and for people who don't shield grab literally everything you do, a short hop bair and a full hop bair can be interchangeable.
Use upair. I cannot stress this enough. Too many Falcos neglect this move. However, again, don't get predictable.
In the same vein, use reflector. Not only does it reflect projectiles ("WOW OMG SO SHOCKING!"), it's a decent semi-long-range spacing tool that can catch approaching opponents off guard. (You can also down throw to reflector, and you can also jab lock with reflector, but the lock isn't as guaranteed as a laser, and locks randomly, as opposed to every single time.)
F-smash is a pretty good killing move. Bait airdodge into the ground and net the kill.
Wall jump. Wall jump wall jump wall jump. Wall jump like there's no tommorow, even on a stage without walls, because your wall jump is your best friend, right behind nair. A good way to mix up your recovery is to not sweet spot the ledge with side b but instead go slightly lower and double jump towards the stage, then wall jump onto the stage. Or, once you've grabbed the ledge, drop down, double jump then wall jump and cancel into a side b, which can be used as a mixup to come back on stage or sweetspot the ledge again. Or, for a generally superior mixup for when your opponent expects you to side B, if you have your jump, fake that you're going to go for a side b, then drop down and up b. (^ Opinions. Recover however you like, as long as it's safe.) (Also, if your stage has walls, and the opponent doesn't have a jump, some fun disrespect is to drop beneath them after they use their up b [as long as they don't have good recovery like the Pits, or a teleport], then wall jump [also jump if needed] and dair them. Looks cool, unless you screw it up.)
Perfect pivot laser can stop some opponent's approaches, though usually only once.
Jab and fair can sometimes break out of combos.
In general, try to find a good balance between being defensive and extremely offensive--while being offensive is risky, most non-defensive players are disrupted by your offensiveness. Try to gently and stealthily camp with lasers if the opponent is approaching you (and also shoot them when the opponent recovers high in an attempt to make them airdodge to avoid your shots and force them to dip below the ledge/gimp their jump), grab and dash grab into follow-ups, don't be afraid to jump away out of a combo with your big jumps, use reflector to space, RAR back air, stick to the air keep your opponent's in the air.
ANOTHER LAZY EDIT: Fair has a frame 1 hitbox when you land during the move, which can surprise some people who let go of shield when they're shielding against your fair. You can also drag people down with your fair like Fox does with his fair, but you'll only get a follow-up if the opponent doesn't react fast enough. Speaking of follow-ups, jab into up Smash is a good follow up at kill percent if they don't roll away. If they roll away, punish accordingly. If they don't roll, go ham.)
ACTUAL EDIT: Also make sure to challenge people in the air with your bair, which is the safest choice in any given situation. Fair and nair can be beat out by some moves, such as Pikachu's fair or dair. Bair beats almost everything, is super fast, and can kill at high percents.