I disagree with the above post.
I don't know how you play, so I can't say for certain what you're doing wrong, but there's 3 prerequisites to hitting people in the air:
1) an intuitive feel for your own air movement
2) an intuitive feel for your opponent's air movement
3) an opponent who doesn't see it coming/properly time an air dodge.
The last one is practically guaranteed on inexperienced/new players who aren't used to seeing air attacks (For Fun players, so to speak) so you might find it helpful to practice there (be nice and let them win a couple times if you go the For Fun route, they tend to get frustrated when people like us show up). Be aware that lower level players tend not to have much idea of what to do in the air and better players will move differently.
A lot of new players also air dodge like maniacs as soon as they get knocked off the ground, and if you're playing online punishing air dodging is like punishing rolling...harder and riskier than it should be. Offline punishing air dodging isn't too difficult hence you get mind games to make people air dodge at the wrong time or not airdodge a kill move.
My recommendation is to set the computer to a reasonable level (6-7 or so) where they don't air dodge every time you hit the A button and practice until you get used to your own movement first. To get used to opponent movement you have to play people, but the computer tends to do a good job of not just standing in one spot and forcing you to get used to adjusting your air movement. A bonus to this is that you don't need a friend and there's no pressure to actually win, so you can focus just on air play (and you will lose if you are just playing air, the computer throws smashes randomly and shields with irritating accuracy two things air characters hate). Be aware shields tend to beat air games, so get used to fast fall->grabbing too. If you play higher level computers and they consistently airdodge but you see your hitbox pass their character, consider it a hit.
Also, your character can matter ALOT for how you place and use your air attacks. Diddy is notorious for his quick air attacks with silly range and can throw them out with near impunity. Pikachu has really quick aerials for racking up damage and can also fish somewhat but needs to watch that landing. Donkey Kong has slow aerials that require patience and prediction but can kill like no tomorrow. Look up a guide to your character to know which aerials do what. Be aware that moves with more startup are always harder to hit with when both you and your opponent are moving.