Right now, my training is composed of wifi (I'm at least 2x as bad online as off), level 3 Snake juggling, and watching videos.
Wifi helps you learn the match ups and learn to read, but could hurt your speed and reaction. It can also completely **** up your timing for some combos, e.g. IC CG. (Plus, I get crazy frustrated when I get hit by stuff that I wouldn't get hit offline.)
Playing against CPUs can help your techs and follow ups. As long as you keep the opponent's options in mind, you can even improve your spacing. I might be a bit biased on computer training since I main MK, but I think you can benefit with other characters as long as long as you don't play something like Ganon.
Watching videos help me get closer to understanding what the pros do. It helps with learning match ups, options, and the mind game. Watching videos on characters that you don't play can also help, as you would understand those characters more, thereby helping your match up knowledge.
Lastly, playing offline can be very important ESPECIALLY if you play a character that needs high tech skills and muscle memory. Not practicing that tech skill enough could let you down during a match. (I've yet to become comfortable with my options and am currently working on shuttle loop gimicks near the ledge consistently.)