Marth Tech: Directional Influence
Description / How To Perform
By angling the analog stick in certain directions you can alter the trajectory at which your character is launched after taking a hit. To achieve the maximum influence on your trajectory, the angle held must be perpendicular to the base knockback trajectory of the attack used.
Difficulty: Dependant on Skill Level
Usefulness: 
(Essential Skill)
Survival DI
One of the primary uses of DI is to survive attacks that would ordinarily have KO'd your character. The Blast Zones making up the outer edge of all stages in Melee are square, so the furthest distance from the ground to the Blast Zone is towards the top corners of the stage. Meaning that to maximize your chance of regaining control of your character before hitting the blast zone you should DI towards one of the top corners of the stage.
Combo DI
Using survival DI will often position you too closely to your opponent during their combos, letting them reach you with followups more easily. Your goal while stuck in a combo should be to make it as hard as possible for your opponent to keep you there. In many common scenarios, increasing the distance between you and your opponent during their combos is either the only way to escape, or the best way to make the combo difficult for them to continue.
Extra Info
DI can be used to change your trajectory by as much as roughly 18 degrees in either perpendicular direction.
Trying to DI in a direction parallel to an attack's knockback trajectory will have no influence at all.
There is no 100% guaranteed rule to follow for having good DI, but generally speaking: Use Combo DI to angle away from faster attacks that have direct followups, and Survival DI when hit by large knockback moves or combo-finishing attacks.