Well, you're playing brawl, so there are no combos, and you can live for ages. DI is easier than in Melee. Check this out.
Basically, DI if you think you are gonna get hit. Well, not DI but be ready to DI. You shouldn't be thinking about DI all the time, you should be thinking about it if you think you're gonna get hit (or combo'd in melee). If you're not used to it then maybe you should think about it all the time at first until it gets natural.
In melee you need good DI and reactions. Usually you'll get combo'd, so if you get hit once, you know another hit is coming and you can DI in advance. Brawl is mostly one hit sequences and stuff, and it is slower so no johns, bad DI is unacceptable (unless the game screws you with auto bad DI, which can happen).
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If you've done physics, just imagine that a hit is a force applied on your mass (character) which will cause movement, and you have to counter the vector with a direction in your joystick. The earlier the input, the better the results. Time starts on hit impact, you want your DI to be as close as possible to t=0s.
You want to hold the joystick at a 90 degree angle to your trajectory. If you're flying to the right, technically you're going up-right, so you want to hold up left. Holding up will give more height to your trajectory, and you'll consequently be closer to the stage horizontally. If you were to hold down right, then you'd go really low and you'd fly further away from the stage.
If you're going straight up, you want to hold away from your opponent (or towards for tricky knockbacks like marth's up tilt). You can't DI down btw. This will give your trajectory more horizontal movement, and won't get you as close to the kill ceiling.
When you get hit, you have to momentum cancel. I haven't played in a while, but iirc there's a trail of white smoke that follows you when you fly away. You can move after the trail of smoke has ended (or mash, since you have 10 ****ing frames of buffer, gosh what a stupid game). You have to do your characters' fastest aerial to cancel momentum (not the one that comes out the fastest, but the aerial with the shortest duration total). Jumping also help reducing knockback considerably, but you can't jump as soon as you could attack or airdodge. Airdodge doesn't help at all except for a few select characters.
If you're going upwards, you want to fastfall an aerial to momentum cancel. Most character will use dair, but in some cases you want to fastfall your fastest aerial (like momentum altering dairs will actually kill you faster). Remember that pressing down on the cstick automatically fastfalls, but it will not fastfall if you're holding down on the joystick as well.
Mind you, I have not played the game much lately, this info was good a few years back. Still seems good though.
And I helped someone for the first time in years on these boards.