When you get knocked off the stage, the situation seems pretty helpless. But nothing is further from the truth. Here's how to get back to safe ground in a few easy steps.
Don't worry! You're not done yet, Mario!
Every character has two jumps (or more), so what you're going to do first is execute that. It will lift you up quite a bit. Be sure to aim for the stage too, because you're really going to need the horizontal distance.
You've intercepted the knockback.
One last critical move rests. Use your Up Special Move to recover back to solid ground. Note: Some Up Special Moves won't give you enough distance either vertically or horizontally - make use of different Special Moves.
Mario's Super Jump Punch works well as a recovery move.
There you have it. It's important to know that there are methods to recover that are way beyond what I described here. These can be seen as Advanced Tactics. Remind me to get to that sometime.