My technique:
First, ensure the plant has properly rooted out it's current pot. Most people transplant far too early, and lose one of the main benefits of incremental pot-ups by doing so. Forget this "rootbound" business. It takes a LONG time for a plant to become rootbound.
With that said, I always transplant when the soil is at it's dryest part of it's cycle. I lightly squeeze the sides of the pot to prevent sticking, then i hold the base of the plant's stem, and simply pull the pot gently downwards and off. The dry soil ,combined with a well-developed root mass, ensures that everything stays in one piece.
I then place the entire mass into the new pot, which will have a pre-made hole in the soil, using the previous pot size as a template. The plant spends all of about 2 seconds exposed to the air. I then water the plant thoroughly.
Note that I make no mention of turning pots upside down, as I see this as a pointless step. A good root mass will hold itself together anyway, especially if the soil is dry. I have done many transplants using this method, and have never seen "transplant shock", ever.
