Don't play on FD is my best advice.
Most of the time you are going to have to take the punishment and learn how to weave yourself through platforms and catch your opponent in between.
If it's ranged characters like the space animals/ice climbers, Samaus/ZSS, Mario, Luigi, Kirby, Pikachu, Lucario, Squirtle, Ivysaur, you can still approach most of the time through the air/roll dodge. If they just keep pressing B or whatever it's used, it's easy to read. If they know when to, you're going to have to do roll dodges/SHAD's here and there.
Characters like Peach/Link/TLink can be approached with what I mentioned above, but as well with a dash attack if you pressed A while they threw it at you. Of course, going to have a harder time with the Links.
Don't know much about Dedede.