Errr... technical Falcon? Okay =P
Short hop reverse needle cancel bair is pretty hot.
Mess with his movement game with your needles. Your nair should eat through most of his aerials, so be ready with that. Tilts are good to use too.
You can crouch cancel his aerials at low percents (uair and nair, anyway) and then get a grab from there.
Mostly what you're looking for is a grab. Once you get that, you can tech chase to victory.
DI away from him for the grabs. Don't be predictable with your techs. When in doubt, tech straight up and buffer a spot dodge or the like.
You could also try some randomly tricky things like... hold your shield against his incoming aerial, then wavedash out of shield under it before he connects, then grab him from behind. I dunno. Lots of options.
Platform camping works too, depending on the stage.
If you manage to trap him, you can harass his shield with a spaced bair, then run in with a grab.
You should make sure your edge guards are flawless, too.
For a good example, watch Mew2king gay up Darkrain. Sheik is gay. If you're not winning, it's because you're not being gay enough.