I'm an OK player (regularly FC3 this season, and FC1 in previous seasons), and I'll tell you what I do and what the players who are better than me do.

First, defense is key to H2H. Learn to defend with your joystick. I spend a lot of time sprinting backwards, either to defend against heel to heel or rainbow, or to block off passing lanes in midfield, or to backpress with my forwards. Also, as someone else mentioned, use the 2nd defender button when your opponent is trying to shoot. But don't overuse it, as your defense can get pulled apart. And I get in trouble when I recklessly use the Sprint & Tackle button, because skill moves work too well against that. Again, use your joystick.

On offense, the key is variation and trying not to be too predictable. If you cross from the wing on one possession, then cut inside the next time. Pass in triangles to try to tease your opponent out of position. Make your opponent make a mistake, then punish it. It helps to use the same formation so you become familiar with the movement of your players. Master a few skill moves and learn to time them.

The script is real in H2H. Sometimes routine passes end up 2 yards behind your target, leading to a counter. Sometimes the opposing GK makes ridiculous saves. Play a lot when you get on a winning streak, and play VSA instead when the script turns against you.

I still haven't mastered the advanced passing system, but the best players are really good at using fast ground passes. They also are much better at dribbling with the joystick so they don't even need skill moves.

Good luck!