As an Ike main (mostly Ike examples following), I use Eruption so that the sword will hang off the edge, and then follow-up with an attack when they are launched upwards (this was very difficult in Brawl due to stronger edge sweetspotting). I also will go out and Fair if necessary (it works most of the time). Down-tilt is also great for people who do not sweetspot the edge right away, especially effective against Little Mac, pushing opponent out horizontally (I wish it still Meteor Smashed, but it's much easier to hit in this game and would be broken if it did). Dair is also an obvious option, and it's easier to spike with in Smash 4, because unlike Brawl most of the hit actually spikes now, but it lost a lot of range. The Reverse Aether Spike done without SDing is now impossible because Ike can no longer recover in reverse with Aether, but it will still spike HARD. Instead the safer option is go off the edge and recover normally with Aether. If Ike hits the opponent this way, they will be spiked HARD. Aether on the stage to catch opponents who decide to go over the edge isn't a bad way to deal damage.
If I feel like catching someone off guard, I will jump onto the edge and ledge trump them and then follow-up the best I can with maybe a Bair. If it fails, it'll at least leave them shaken up a bit, feeling a bit less secure.
If the person has made it to the edge, I will predict which recovery option they will take from there and punish it. Most people will not go for the jump, and will instead go to a roll or stand-up/attack, so I punish with a Fair as it leaves me the least open if it fails. People who hang on the edge too long can be hit, so a Fair to the edge works at that point too.