Summary
After connecting with a Launcher and going up into the air and, during your Air Combo, press Toward or Back + Special for a side Aerial Exchange, Down + Special for a downward Aerial Exchange, or Up + Special for an upward Aerial Exchange. Aerial Exchanges are free and cost no Hyper Meter to perform.
Aerial Exchange Mechanics
Whenever you land an Aerial Exchange, what will happen is that your Point Character will tag out and Assist Character 1 will jump into the game with an automatic attack. The character jumping in will almost always come from the other side of the screen so that, if you were facing right, the new character will jump in from the right and now be facing left.
The automatic attack from your new character will hit the opponent and can be chained into any other air Normal Move you have and, from there, your character will adhere to the normal rules of Air Magic Series. The Automatic Attack, it should be noted, causes a Soft Knock-Down where the opponent spirals in the air until they hit the ground. In some cases, with character like Wesker, you can connect with the automatic hit and cancel it into a teleport that brings Wesker to the ground and this allows you to Juggle the opponent from the ground before they land because they will never recover in the air. However, there is no room for OTGs because it is a Soft Knock-Down so they will roll the instant they hit the ground.
Immediately moving to the ground to do a relaunch may not be the best option in some cases, though, because Aerial Exchanges cause a large amount of hit stun deterioration, but all hit stun deterioration is ignored before your character reaches the ground. Characters that can do long strings of attacks during an air combo, such as MODOK, can take advantage of this and do a great deal of damage before they reach the ground.
The new character coming in can also perform yet another Aerial Exchange during their Air Combo. This will cause the new Point character to tag out and bring in Assist Character 2 as the new Point Character! Once he or she has tagged in, however, you can no longer perform an Aerial Exchange. Like DHC's, you only get two in a sequence. If you manage to land and relaunch into an new Air Combo, however, you can actually start a new set of Aerial Exchanges.
If one of your characters has been K.O.'ed, however, that does not change the number of Aerial Exchanges you can perform. You can still pull off two Aerial Exchanges in a row, you'll just jump from Point Character to the remaining Assist Character and then right back to the original Point Character. This can actually can be an advantage if you want to gain meter from a series of Aerial Exchanges and keep your original Point Character as the Point Character.
The Ups and Downs of Aerial Exchanges
There are several differences between the different directions of Aerial Exchange. The move that comes out when you perform an Aerial Exchange is predetermined and, in general, attacks in the direction of the Aerial Exchange. For example, Iron Man's three Aerial Exchanges are his three different air Hard Attacks where he shoots a small beam from his hands straight, upwards, or downwards. This means you can't actually just pick a direction and have it guaranteed to land every time. If the opponent is too far above you during the Air Combo, your downward Aerial Exchange attack can actually miss! However, if you are even height with the opponent, all three directions will almost always connect.
The upward Aerial Exchange pops the opponent up higher into the air. So if you do two upward Aerial Exchanges in one sequence, you will end up very high in the air and, if you land an Air Combo Finisher, you'll see that the character has a long way to fall. This means your character also has a long way to go before they land back on the ground, but your falling speed is usually slightly accelerated when you perform an Air Combo Finisher that far up into the sky.
The sideways Aerial Exchanges will be the same whether you hold Toward or Back: there are no differences between the two. When you connect one of these, the opponent will be launched into the opposite wall for a Wall Bounce and the new character jumps in and will tag them off the Wall Bounce. This will generally keep the opponent at the same height you were already at in the air.
The downward Aerial Exchange will knock the opponent downward for a Ground Bounce. This means that, in general, you stay closer to the ground when the new character jumps in. Thus, if you have combos, such as X-23's post Air Combo Finisher OTG with her fully charged Ankle Slice, you may only be able to perform it after a downward Aerial Exchange because the other directions cause X-23 to be too high into the air to land and fully charge the Ankle Slice. And even if you performed an upward Aerial Exchange the first time, if the second Aerial Exchange is a downward one, you'll reset your position all the way back down to ground level because the opponent has to reach the ground for the bounce.
Exchange Rates
Finally, the last major difference between the three different Aerial Exchanges are that different directions give you different Hyper Meter boosts. Sideways Aerial Exchanges give you half a Level of Hyper Meter when they connect. Downward Aerial Exchanges give you an entire Level of Hyper Meter when they connect. Upward Aerial Exchanges, however, give you no Hyper Meter bonuses whatsoever, but that is because, in general, upwards Aerial Exchanges do the most damage by around 10,000 points of damage. But if you need to build up Hyper Meter, Aerial Exchanges, particularly the downward ones, build up Hyper Meter faster than any other method in the game.
In addition, different directions of Aerial Exchange give damage bonuses to attacks that follow in the combo. Downward Aerial Exchanges do not give any bonus, but sideways Aerial Exchanges give a 25% damage bonus and upwards Aerial Exchanges give a 50% damage bonus. These bonuses stack with each other multiplicatively, so if you do two upwards Aerial Exchanges, you will be getting a 125% bonus and two sideways Aerial Exchanges give a 56.25% bonus. A sideways and upwards combined gives a bonus of 87.5%. If you relaunch, the bonuses will continue to accumulate after a new set of Aerial Exchanges. The downside of this is that the bonus is applied before damage scaling minimums, which many characters reach very quickly, so most of the time the bonus won't be apparent. By using the DHC trick to reset damage scaling, though, you can retain the damage boost you built up before hand and apply it to the next part of your combo.
Strategy Corner
The different amount of Hyper Meter gained definitely makes 
Aerial Exchanges more preferable than the other directions. What this does is it creates a weighted game of Rock Paper Scissors to play when trying to 
Aerial Exchanges. Obviously, people will prefer doing the Aerial Exchanges, but that makes it the most obvious to use and, thus, the first option to try and counter. So players may elect to go for the sideways Aerial Exchanges and go for a little less Hyper Meter so it's not as obvious to counter. However, you can start predicting that and go for the sideways if you've countered the one enough times.
And if you really just want to change characters and don't want to risk getting countered, performing an 
Aerial Exchange might be the best option. Opponents will least likely be trying to that option because you get the least benefits from that (10,000 damage compared to a full or half a Level of Hyper Meter). But that means it's usually open for you to use without being countered, so you can more safely tag a character who may be close to being K.O.'ed out.
So it's really not about a guessing game where you have a 33% chance of winning. Because each direction yields different results and there is a preference order in which you would like to land them, it creates a bit more of an involved mind game than just random guessing.
Ignoring the Limits
There is a rule in the game that prevents multiple Ground Bounces or Wall Bounces in one combo. This is ignored for Aerial Exchanges as they will always cause a Wall or Ground Bounce when they are supposed to regardless of what's happened in the combo beforehand.
Aerial Exchange Counters
The biggest weakness of Aerial Exchanges is that they can be countered. The game has a system of Aerial Exchange Counters built into it that allow opponents to sabotage your Aerial Exchange! Right when you press the button to perform an Aerial Exchange, there is a very small window during which, if the opponent holds the same direction as you and presses their Special Button, they will perform their Aerial Exchange Counter. What happens is that they will stay in the air and look like they discharge energy from their body and your character will get hit and bounced into the opposite wall and then drop to the floor. You will not get the character switch as a result and you will forego any Hyper Meter boosts as well.
However, the counter is the extent of the punishment you will receive. The wall bounce that occurs off of the Aerial Exchange Counter is different than the standard Wall Bounce in that the character falling off the wall is completely invincible until they land. Also, it's a Soft Knock-Down so they will perform a roll the instant they hit the ground. You cannot be further punished then whatever damage you take from the Aerial Exchange Counter.
Note that the sideways Aerial Exchanges can be countered by either direction. If you performed it holding Toward, they can counter it holding Back or Toward. Also, the window in which you are allowed to counter an Aerial Exchange is extremely small, so while you may be able to input more than one counter direction in that window, it's very difficult to do so.