You can alter your launch trajectory after a hit by pushing the analogue stick in specific directions. This is called Directional Influence (DI). To maximise this influence, hold the stick at a right angle to the base knockback angle of the attack.
One can use DI to survive attacks that would normally cause a KO. The blast zones on the outer edges of all stages in Melee are square; the furthest distance from the ground to the boundary is towards the top corners. You should direct your character towards a top corner to maximise your chance of regaining control before hitting the blast zone.
Survival DI often keeps you close to your opponent. This proximity allows them to easily hit you with subsequent attacks. If an opponent is comboing you, you'll want to make it harder for them to continue by DIing away to create distance.