Summary
To perform a Delayed Hyper Combo, first perform a Hyper Combo with your Point Character. Then, while the Hyper Combo is still being executed (even before it hits or during its recovery), perform the command for any Hyper Combo that the current Assist Character 1 possesses to cause the Point Character to leave the battle and have Assist Character 1 to jump into the screen and perform the Hyper Combo you executed. Then, while the second character is performing their Hyper Combo, you can choose to enter the code for a Hyper Combo possessed by Assist Character 2 to DHC into the third character.
The ABC's of DHC's
You can only do up to two DHC's in one sequence. However, if you allow a Hyper Combo you DHC'ed into to end and are able to continue combo and then activate a brand new Hyper Combo, you can start the DHC sequence from scratch and get up to two DHC's again. However, you have to have enough Levels of Hyper Meter to perform this, as each DHC costs as much meter as it takes to perform the Hyper Combo you've DHC'ed into.
If one of your characters has been K.O.'ed, however, DHC'ing will obviously always bring in the character who is still alive regardless if they are Assist Character 1 or Assist Character 2. And even though you are missing one character, you are still allowed up to two DHC's in one sequence. So if you have two characters left, the Point Character can DHC into the remaining Assist Character and the DHC once again right back into the original Point Character.
And it goes without saying, but it's being said anyhow, if you are the only character left on your team, you cannot perform a DHC.
DHC's Not Easy As 123
The most obvious use of Delayed Hyper Combos is to extend Combos and cause more damage. Oftentimes, a Combo that ended with a Hyper Combo will fall just short of finishing off an opponent's character. And because a lot of Hyper Combos cannot be followed up with more hits, a DHC is usually used to finish off the opponent's character.
Keep in mind that, just because you cancel one Hyper Combo into another via DHC, that the second Hyper Combo will connect. Thanks to the sheer variety of Hyper Combos, most DHCs will more than likely miss! But because you can DHC at any point during a Hyper Combo, you can usually adjust the timing so that the Hyper Combos do connect.
For example, if Chun Li lands her Hoyokusen, the last hit launches the opponent up into the air. So if you DHC her Hyper Combo after the last hit into, say, Deadpool's Happy Happy Trigger, Deadpool's Hyper Combo will miss. However, if you DHC before the last hit connects, because they are still on the ground, Happy Happy Trigger will actually connect.
Another example is with Amaterasu and Morrigan. If you land Amaterasu's Okami Shuffle and want to DHC into Morrigan's Finishing Shower, you have to DHC very early, right when the lightning portion of Amaterasu's Hyper Combo begins. However, if you want to combo into Morrigan's Darkness Illusion, you have to DHC later in the combo, right when the lightning portion is about to end. So even with learning to DHC into the same character but different Hyper Combos, different timings will needed. It will take a lot of experimentation to figure out how to combo Hyper Combos via DHC.
DHC Tagging
However, DHC's actually have what can be argued as an even more important use than just landing combos. The most important thing that DHC's allow for are a safe way to swap characters. So even if your opponent blocks the DHC, if the DHC is safe on Block, you can actually use two levels of Hyper Meter to safely bring in Assist Character 1 as your new Point Character. Performing a normal Cross-Over Attack can be risky as the character coming in is at a huge delay if Blocked. And landing an Aerial Exchange requires you to start landing a Combo and, oftentimes, you need to swap character right away in order to save your Point Character, so waiting until you land a Combo isn't practical.
And oftentimes, people won't even bother to try and land the first Hyper Combo. If you have one that starts almost instantaneously, players oftentimes will just activate it as soon as they are free and instantly DHC into the second Hyper Combo without even worrying about letting the first Hyper Combo animate at all just to guarantee the Point Character tags out.
So DHCs ends up being one of the safest means to tag out your Point Character. And not only can it be a safe way to change characters, it also prevents the character entering the match from losing their Red Health, which is a huge bonus.
Strategy Corner
SAVING YOURSELF FROM PUNISHES
Level 3 Hyper Combo DHC'ing
One restriction of Delayed Hyper Cancels, however, is that while you can DHC into a Level 3 Hyper Combo, once a Level 3 Hyper Combo connects, you can no longer DHC out of one! Whether this is the result of the developers thinking that canceling out of a Level 3 would be too powerful or because the fancier animations of Level 3's prevented a simple way to have DHC's work off of them, it's just not possible without any exceptions.