We have a wall-sized sliding glass door that opens up to the deck, with bird feeders. That said, we get a lot of birds that fly into the window.
You're right; you're not supposed to stress them out. What we do is scoop them up, put them in a dark(and heavy, so they can't get themselves out) box. We leave the bird in there anywhere from 30 minutes to an hour, depending on how much damage they did to themself. The first bird we had that hit the window we brought to a Rehabilitation Clinic, and she wormed the poor guy, and did all kinda of hands-on things, and he died. The best thing to do is leave them alone.
Earlier today, as a matter of fact, a finch hit the window. It was my first time actually getting to the door faster than anyone else to pick him up, and he didn't look good..he was really out of it and limp. He was in the box for like 40 minutes and started chirping and flapping around to be let out. Since we've used this method, we've had a 100% success rate.