I pretty much just move around, letting my ineffable instincts guide me to the tactically best location to be currently standing, and then choose moves to respond to the relational configuration of the two characters and the current terrain dynamic.
I suppose you need me to expand on how I choose the move, then. Well, I tend to go for a direct approach - to hit the guy. No funny business. I rarely try to manipulate my opponent around. At least, not consciously.
It arises, though (I can tell from playing Melee and analyzing myself consciously), that my attention to where the characters are standing eventually seeps into my procedural learning, such that I actually will use moves that put me in a better position, by putting other-guy in a not-better position.
So yeah... I aggro, I guess? I mean, unless my opponent has this really weak, sort of predictable style for which I know the best approach is to take it safe; I assume override control of my hands and really think out the match. It quickly becomes clear whether I can punish the opp for being all flash and no substance.
For me, I started out using hit-and-run tactics with Sonic and ranged attacks with Lucario. However, in preparation for this weekend, I've been trying to refine my playstyle with my mains. I want to play more conservatively with both Sonic and Lucario, so I've been using counter-tactics and mind games, but I still have a lot of practice to do.
To say something here, Sonic really runs contrary to my instincts, because his speed allows him to be standing pretty much anywhere you like at any time. I'm not used to that - I'm used to having to settle for 'the best place you can move to in a split second'.
From watching Sonic games, though, I can tell you really want to use that awesome run, to
(a) Withhold information from the opponent, specifically as to when and where you'll choose to strike (run. stop. run back, turn around. stop, run. Attack. Run. etc.)
(b) Dodge attacks (many cases it's better than an actual L-dodge, I've noted)