My suggested strategy with the Hori protectors is thus:
1) Before you even begin, have the yellow cloth that came with your protectors, a can of compressed air, and a scotch tape dispenser right next to you.
2) Open your system and assess both screens. Sometimes in the product testing process, finger prints can end up on the screen. Check for those, and for smudges and skin oil and whatnot from the testers. If something catches your eye, wipe it with the yellow hori cloth. If the screen looks very clean, don't wipe (the cloth can generate static, which can attract dust...if the screen is pretty damn clean you're only making a headache for yourself if you anally try to get it somehow even cleaner)
3) Make sure you have the protectors laid out so you know exactly which is for the touch screen and which for the top screen. Make sure they are ready to go, and that you've read all the other instructions in the hori packaging.
4) Give the screen you're applying to a good blast of compressed air, and then grab the appropriate protector and apply as intructed by the packaging. If you see you're about to catch some dust when you have one corner down and you're bringing the rest of the protector down, grab the air again and blast away, and then drop the protector and assess the situation.
5) For bubbles which clearly have some dust at the heart of them, grab a piece of tape, and gently...GENTLY lift up the nearest corner of the protector...when you get it up enough to get the dust, either blast it with air or use another piece of tape, carefully so as to not stick it to the screen or protector, and that way you can just let the adhesive of the tape get the dust.
6) For all other bubbles, just use something to dull the pressure you're about to apply, like the plastic sleeves the protectors come in, and just rub slowly, patiently, and very gently WORK the air towards the nearest edge of the protector.
7) Lastly, wipe your own fingerprints and skin oil off the protectors, see if its all good, and then start playing.
8) To straighten a crooked protector, just use the tape to get it up and realign, but you'll have to go through all the same procedures.
9) I'm never writing these steps again.