Go to the training room, play around with the character, see what their moves are. What's good, what's bad, where they like to be, and figure out where you have the advantage. Make the unfamiliar familiar.
For example, it you use Little Mac for a bit, you'll find his smashes has super armor, and hit tilts are fast and good combo starters. You'll also learn you suck in the air and off-stage and need to be center stage on omegas to play to your strengths. This means you don't do well vs grabs and get juggled or being tossed offstage. You will also find you don't have a great grab, so you don't do well vs shields.
So now you look at Link's kit. Link has good juggles that come off of a tether grab, and he's pretty good offstage. So you can shield and grab him, or grab him on his dash in, and juggle Little Mac. Or stay near the edge where he doesn't like to be, and toss him off-stage for an edge guard. If you're a Mac Player, you might want to stay center stage, but Link has projectiles to force an approach.
If you want to know just how to fight a character the moment you meet him, you might try observing the player and checking out their individual habits, or trying Link stuff and seeing if they have character knowledge or counters to your usual habits. You might also try fighting around global rules. For example, timing your attacks when they land off a jump, to punish the obligatory landing lag. Tech chases, roll punishes, ect.
I try to feel out opponents by throwing some projectiles at them to see how comfortable they are shielding and power shielding, and using the jab cancel to see if they're a button mash, or they know if they can react after the second jab to inform me of how I'll need to play. Down throw once to see if they know how to DI correctly. That lets me know how much they know the match up, how much I can get away with, and give me some tendencies and habits to work with, as well as a general idea of their skill and adaptability so I can make educated predictions.
Checking out the Metagame and Match Up threads on this board is also helpful, and I think those are the right places for this discussion, come to think of it.
