What little I played from a rent, I got raped by Galactus, suck with Zero, love Dante and cannot get an air combo going worth a damn.
So when the time comes, I am ready to bring the suck!
It's real simple. Smack them up to the air with X (Special) then, the usual pattern is Med, Med, Heavy. Depending on the character, here is where you can change things up three different ways.
1) You hit X again and your opponent slams down into the ground. If you land fast enough, you can call a partner to hit on the ground (OTG) and try to reset the combo or you can use a special (Zero's Rekkoha, for example.)
2) Hit X while holding a direction to tag in a team mate. Depending on the direction, one of three things will happen:
-2a) Hit Up+X, you'll smack your opponent higher into the air. This one does the most damage.
-2b) Hit Left/Right+X, you'll smack your opponent off the wall. This one does less the damage, but is quick to pull.
-2c) Hit Down+X, you'll slam your opponent into the ground, who will then bounce back up. This is the weakest one damage wise, but it automatically gives you one bar of Hyper Gauge for free. People with Phoenix on their team love to use this one.
When you do any of these, you're free to repeat 2 again to tag in your third partner, then choose to go either step one or step three, which is...
3) Hit them with an aerial hyper. The fortunate part in this game is that hypers in this game are always Hado, Back Hado, or Shoryu inputs with two attack buttons. From here on, you have even more options, like entering another hyper input during the one going to tag in a partner and have them perform their hyper. This doesn't always works, like during certain cinematic hypers (Dante's level 3, for instance.) You can even X-Factor to cancel the hyper and pull it off again, but using X-Factor is a whole separate topic.
tl;dr: anyone can do an air combo easily and the variety of options opens up the potential quite nicely.
Honestly, just like I learned in Tatsunoko vs. Capcom, the best friend you have in this game is training mode and just dicking around in there. Mission mode can also help, but some of the later ones get frustrating in that you need to be familiar with the character and the general game engine to pull off some of the combos.