I peronally like to follow them facing forward, using nair to catch them out of whatever, since it has a long hitbox, like Jackson described. I use Bair for stagespikes, and Nair for followups (after u hit them with nair).
Also, if you have a bit of fear going off the edge, you might just use your specials. They feel like they were made to edgeguard.
Needels (and shorthop needels...) are good to steal double jumps or hit opponents out of their recovery move, causing them to screw up their recovey (melee shows great examples of this). The side B (the bomb thingy) does good damage and knockback, and might scare your opponent quiet much (throw it close to or over the edge, wonders will happen).
And then theres the bouncing fish. Try to read your opponent and land one of those on them. Hit this offstage and its usually over. This move is so ridiculusly good. You can do it from the stage or in the air, while chasing your opponent, also, Fair, Bair, Nair into fish.
Just try not to get stagespiked, and never ever use your Dair. This happened to me so many times thanks to that D-pad.