Who do you tend to play? Pit, I assume? Some characters can break out of being juggled a lot more reliably than others.
Well, he says "with any character," so any general advice would be useful too. I feel the same way, but things I've learned recently: 1) you can fast fall after being hit instead of tumbling down, 2) if they're mid combo, you can hold down shield to do an air dodge at the first possible opportunity. If their combo is true, you won't be able to air dodge or avoid the combo, but if it's not true, the air dodge will break the combo. Also, and this is obvious, you have to DI (directional influence) in a smart way to avoid your opponent.