Survival on a technical level:
You get hit. Both the attacker and the victim are frozen in hitlag (only the victim if it was a projectile). During this hitlag, the victim can utilize directional inputs to SDI. SDI is a short teleport in a direction of the user's choosing (if you are hit off the ground, down is not an option). The best way to do this is to wiggle the control stick between two adjacent inputs (such as right and up-right, as an example). Some people refer to this as quartercircle DI or QDI; I find the term misleading and unnecessary (the phrase "DI" is overloaded enough). At least anyone who didn't know before knows what it means now. For most hits, it isn't really worth going for SDI since the survival benefit is fairly small; the main use is to escape multi-hit moves.
On the frame hitlag ends, you should be holding a direction. This direction will be your DI direction (that's just normal DI). You can't oppose the knockback directly, but you can use DI perpendicular to the initial launch vector to change the direction. For a simple example, if you are hit straight left, you can't DI right to slow yourself down but you can DI up to make yourself fly up-left at the same speed you would have flown left with no DI. You want to try to aim for a corner; since the stages are all rectangular, this maximizes the distance between you and the blast zone you're flying toward.
You enter hitstun immediately at the end of hitlag. After hitstun is half finished, you are allowed to either do an aerial (the normal aerials you can do with A or the c-stick, not specials), a tether attack ("zair" is a common name for them), or airdodge. You can buffer this so don't worry about the timing. Doing an aerial immediately allows you to begin fastfalling (including during the start-up); doing an airdodge (or tether attack? not 100% sure but mostly sure) makes you wait until the airdodge finishes. I should note if you use a tether attack and it grabs the ledge, this instantly stops your flight and is a good thing to go for with the four characters able to do it (utilize DI down to make it more common). That being said, the generally best plan is to use the aerial that FINISHES the fastest. It does not matter when the hitbox comes out on your aerial; it matters when the aerial finishes executing in the air (as in when you're allowed to do something else after using the aerial). Immediately upon doing it, hit down to begin fastfalling (you hopefully used your DI to aim a little more vertical than horizontal). The fastfalling basically makes gravity stronger on you, and gravity can oppose your launch force directly. If you wanted to use a down aerial, you can just slam down on the c-stick and exploit the automatic fastfalling on c-stick down aerials to your advantage (this is sometimes the easiest way to survive even if you have a slow down aerial). It should be noted that while being launched, aerials with special momentum altering properties (such as Sonic's down aerial, R.O.B.'s back aerial, or Lucario's down aerial) lose those properties. Do not consider them when deciding what to do. A last note is that if you're holding an item (such as a turnip from Peach), throwing it still replaces your aerial like it normally would, and throwing items tends to be a very quick thing to do.
After the aerial finishes, you gain the ability to do midair jumps and special moves (and, contrary to some rumors, you do NOT regain air control, the ability to steer yourself left and right in the air with directional inputs). Unlike with normal aerials, some specials can alter your momentum while you are being launched. The most obvious examples are Mr. Game & Watch's Oil Panic (not the fully charged version), Yoshi's Egg Roll, and Donkey Kong's Spinning Kong as those stop the user completely. Some others have effects too; for instance, Fox's Reflector totally cancels the vertical component of his momentum (but he can continue to fly left or right). If you have a relevant special that will help in your situation, now is the time to use it. Otherwise, you probably want to do a mid-air jump. In general, midair jumps help you survive, but when you do one, you do receive a very small boost away from the stage. If you are nearly stopped and very close to the blast zone, you shouldn't use one. If you're traveling more quickly or are not very close to the blast zone, you are safe using one and will likely benefit. Of course, once the second half of hitstun finishes for real and you stop flying, recover as normal since you aren't flying away anymore and have normal control of your character (including air control so you probably want to be holding toward the stage by the time you get to this point).
That's about it for survival though there's one more thing. If you were hit by a meteor (an attack that launches you straight down), when hitstun is half finished, you can input a jump immediately at that point (don't do an aerial), and it will cancel all launch force. This is "meteor canceling". You cannot buffer this, and if you press X or Y before the halfway point of the hitstun, X and Y will not be accepted for a meteor cancel input at any subsequent point in that particular launch. You can still meteor cancel with tap jump though.
I suppose I could also talk about things like teching, but that is getting into stage geography and survival which is beyond the scope of this post that was already beyond the scope of the original question. The simple answer to the original question was "frequently but not always".
