Note that all of this is from my own experience. If it's wrong, then sorry, I'll fix it.
I agree with what others said. But also keep in mind the mindset required when playing spacies, and try not to get discouraged if you get bopped, especially early on. Sometimes you just get gimped on FD at like 2%. Sometimes you'll pull a sick 0-death and take a stock in 4 seconds. Just keep on trucking, focus on the present moment (in matches and outside), iron out rough techskill, work on consistency, and the payoff will be fantastic.
I would learn how to control the bird first. It's the basis for everything else you will learn about neutral and punishment, so it's best to start now so you'll feel nice and cozy, since Falco has such a different rhythm compared to other characters. Most of the people in my fledgling scene have never even bothered learning techskill or advanced techniques, and because of that I can consistently beat them just because I feel more comfortable with my character than they do.
Don't forget about your tilts. U-tilt is an amazing tool for starting and continuing combos, and creating a defensive wall along with b-air, d-tilt can kill at high percents and can sometimes be used when trying to wall out aggressors, and f-tilt can be used for edgeguarding with it's multiple angles. A lot of Falco's forget about U-air it seems, which is a shame since I find it is excellent at extending combos, and from my own experience works extremely well at killing floaties when it sweetspots. But also keep in mind to get creative with his moves, they have a lot of uses that you can use to surprise your opponent with.
Lasers are good. They can pin opponents down, force them into bad positions where you can go in with a shine/grab/laser-grab/etc. and start a combo, condition them into patterns you can exploit (by mixing up rhythm of DD/movement with lasers, approaches, laser timings, etc.) edgeguard, extend combos, safely move around (
when spaced well) with the fantastic options they provide for movement, etc. They rock, but make sure you don't over rely on them like I did (and still do lol).
I like to make absolutely sure I have won the neutral before I go in. Falco gets punished insanely hard, and playing over-aggressively in the stupid way is a great way to get punished.
Read about Falco. There is plenty of information on the discussion threads to be found. Here is an excellent Falco doc i keep bookmarked:
https://docs.google.com/document/d/1wDdb-kNgCaZ-zTBFL33rrs3bcPjRWpEnXHegYCIaO5o/preview
Have fun playing the (imo) funnest character in the game!