for universal basics, practice shffl's.
short hop, fast fall, l cancel (all in relation to aerial attacks, not specials). every character is going to use this, in some form or another.
and when i say practice, i mean literally practice it. go into training with your character of choice and just short hop until you're at around 90% consistency (so 9 out of 10 times). if you've already got that down, make sure you can fast call consistently (shouldn't be too hard, but the ff timing can get thrown off during attacks, because of hit stop).
then work on your basic l cancelling, where you don't hit anything. then move into lcancelling when you're hitting a cpu and get used to changing it up. then, you need to work on hitting shields, which is a slightly different timing. i've heard someone say that he likes to set damage ratios so the cpu has a 9 and you're a .1 or something like that? so they basically don't move at all when you hit them, so you can just stand there and wail on a lvl1 for a long time without worrying about killing it.
that's the most important set of skills to learn, since every character in the game is going to use them. after that, learn your dash dance spacing and timing and watch
https://www.youtube.com/watch?v=RfBuAo_Bfvw&index=4&list=PLqcfzvwmeIM_bjtHGSCDWlggTWe8ZisBj to learn how to implement dash dancing properly. after that, it's going to be mostly character dependent, so look into your character's forums and ask around there about what's most useful.