To do a Team Aerial Combo, you launch an opponent into the air, hit them with 3 hits or so, then press a direction + button(). This creates an attack where, if it connects, you tag out to one of your other teammates to come in and continue the combo, and you'll also gain some meter (except on Upward exchanges). You can do this one more time to create a combo with all 3 of your characters and gain some meter for Hypers.
Now, to do an Aerial Counter, you have to anticipate when your opponent is going to attempt an aerial exchange, and then you have to press the same button press that they do! You also need to have at least 1 hyper meter stored to perform an aerial counter. Now, this requires some prediction and possibly knowing the character they're using, but your best bet is to wait for them to hit you 3 times in the air, and then press + . A downward aerial exchange will grant you a full bar of hyper meter if it connects, so a 3-character air combo can get you 2 free bars. So this is most likely going to be the attack they attempt to tag-team air combo you with.
The attack that creates a team air combo is signified by a quick flash of darkness and a bit of an orange glow, kind of like a snapback. That quick moment of dark flash is where you need to press the Down + (or + , Back + , +) , whatever one you think they're about to do) to pull off the Aerial Counter.
You must execute a total of 30 these and they can even be boosted with a friend over Xbox Live! A good method of boosting these with a friend is to choose teams that have support assists such as Morrigan and Amaterasu. That way you can replenish your meter for doing counters. Get your Hyper meters up and do an aerial combo to each other and tell your partner which direction you plan to tag out so that they can press that same direction and counter it.