An important thing to remember is to sometimes not approach at all unless you're forced to by projectiles. You can just sort of run around by canceling your dashes with shield, shorthop aerial attacks, or learn the aforementioned extended dash dancing. The way it works is you input a single dash forward quickly and let go of the control stick, then at the end of the dash input another one forward very quickly in the same direction and immediately after input one the other way. You can keep doing this indefinitely and you can do two or three in the same direction at once etc. The timing takes some time to learn however, it's pretty rhythmic.
Regardless back to what I was saying; not approaching at all and just running around doing stuff pressures the opponent because of how fast Falcon is, the threat of dash attack or dash grab and their constant anticipation. This makes it way easier to eventually catch them off guard with either of those two moves, especially if you stay in mid-range (approximately the distance of Falcon's side b / Raptor Boost). Once you're in that distance, you can also use dtilt to occasionally poke at the opponent, it has pretty good range and sends them in a very bad angle at low %, and kills them at high %. Remember to also buffer your dash attacks in mid range by immediately pressing down on the c-stick (or right stick on Wii U controllers) after you start running. This makes your dash attack come out immediately without the danger of accidentally doing an fsmash. Discovering this was a really big deal for me personally at the time.
Falcon's approach options and neutral game in general are pretty good and underrated by a lot of people, for example in mid range he's the fastest character in the game because of the range of his dash grab, considerably faster than even Sonic if we're counting in frames, although I think Meta Knight and a few others can reach above-Sonic status as well.