Personally I feel like Chaizard is the pokemon I'm most competent with so here's some tips on how to play him.
For neutral, Jab and Nair are some of your most dependable moves. Nair has a large, lingering hitbox and very little landing lag and can even combo into Jab. Jab is very fast and is probably my most used tool as a Charizard main in both Smash 4 and Ultimate. Bair is safe when spaced well but can be played around by good players when you're too predictable with it. Fair is also solid but be wary that it doesn't autocancel from a shorthop anymore. Shielding can be effective for Charizard because Up Smash comes out on frame 6 and gives him a very fast out-of-shield punish. Flamethrower has a slow start up but can be a safe option against a foe who's defensive and difficult to approach. Remember to always mind your spacing and your opponent's shield, Charizard can punished hard if he's not careful.
When your opponent is in disadvantage stage take full advantage of your ground movement to keep them from landing safely. This is your goal as a Charizard player, to hold the advantageous state as long as you possibly can so you can make full use of Charizard's amazing ground speed and large, powerful attacks. Dash attack, up tilt, up smash, and short hop nair are all very effective juggling tools. A lot of them are effective at frametrapping air dodges because of large range and/or little end lag. Since Up Smash is so fast out of shield it can be effective to block and attack from a landing foe and then punish with it. Try to get a feel for when your opponent gets intimidated and starts shielding a lot. Charizard has a potent enough grab game. Even if they're out of d-throw combo percentage you can still use his powerful f-throw and b-throw to get them off stage, setting them up for an edgeguard or free damage from Flamethrower.
Landing can be a little difficult with Charizard so it's important to get good at it. Mix it up with his triple jump, Nair, and neutral and directional air dodges. Be very careful as you land and mind your opponent's favorite pressure tools.
And most importantly, Don't. Flare Blitz. Recklessly. Use it for hard reads and occasionally mixing up your recovery. You might catch some opponents off guard with it when used unpredictably but good players will shield it and punish you for it hard. The other day I shielded one in a Charizard ditto and got a free F-smash of all things off it. It's not a move you should be dependent on for getting kills. Zard has a lot of much safer kill moves aside from it. Like, half the moves in his arsenal kill, so chill out with those side specials already.