There are many tuning medods, but the method I use works extremely well. Of course, the guitar will never be "perfectly" in tune, so if you are in a situation where you need to be absolutely in tune, like if you were recording along with non-stringed intruments, you may have to constantly retune depending on what you are playing: open strings, high up on the fret board, etc.
For normal playing:
When I change strings, I stretch them pretty good by pulling up on the string all the way up and down the neck. New strings stretch considerably at first, so I can't see how a guitar would stay any where close to in-tune without properly stretching the strings.
Tuning: I use a Boss tuner. Most tuners will work equally well, some more accurate than others. I constantly pluck the open string about every second whilst tuning. As the OP stated, the pitch will fall a few cents flat after plucking the string. With general playing, a note isn't usually held very long, so this is the method I prefer most of the time. There are situations, like when you are recording and you're playing chords or notes where they are plucked or strummed and then held for a long time. In this situation, I'd tune the guitar by plucking the open string, waiting a couple seconds (letting the pitch fall slightly), then tuning the string. Then maybe I'd also tune by the harmonic on the 5th fret of one string and the 7th fret of the next string, just to be sure they are perfectly in tune with one another.
I hope this helps.