I JUST WANT TO LEARN TO DI!! AND I GET EVIL GAY FoXES AND A MILLION PEOPLE MAKING FUN OF ME
Hold down if you're on the ground. If it's a strong move, and it knocks you over, try to tech it.
Hold away if you're in the air being comboed or could be potentially comboed. For a few moves this will fail you (Marth's Dash Attack, Sheik's D-tilt, are two notable examples) but for anything else you will be okay.
Hold up if you want to live after being hit by their combo finisher and then towards the stage but mostly up. The exception is a move that hits mostly up like Fox's U-smash or U-air in which case you DI away.
For Fox's U-throw U-air DI the U-throw one way and the U-air the other.
For chain grabs just slight DI a lot, no DI a lot, and try to be tricky at really awkward times. If they're good this shouldn't matter. If it's a percent-based chain grab like Fox's in the ditto, don't DI (or DI slightly) at whenever it stops to avoid being regrabbed unnecessarily. There's no reason be CGed to 80 when it stops at 55.