There have been some pretty good threads on this issue. I'm no expert on the science, but it goes something like this. Plants outside get blown in the wind and get blasted with lots of sunshine and that stimulates the plants to make a protective "hard" covering or outer layer of cells. Inside a house where the light is gentle and there may be no breeze at all, the plants are not so stimulated, therefore do not grow the protective covering. So hardening off is to gradually expose the plants to breeze and sunlight, so the over a several day period the plants grow those outer layers and toughen up. For very 'soft' plants, I take about 7-10 days for the process, though I have read that it takes less time than that. Also, you can begin the process by placing a fan in the room and letting the gentle breeze rock the plants. Don't blow them too hard though.
I have two techniques. One is to place the plants in the shade with a wind barrier, and gradually move the plants each day, closer to the sun and after a few days totally removing the wind barrier. The plants eventually make it out into the full sun. My other method is to start the plants out in the morning sun, but placing them where the shade overtakes them after an hour or two. Each day the plants are moved a little further out from the shade so that the sun exposure time is increased a bit each day. These plants eventually get move far enough out that the shade no longer over takes them. Well before then the plants have already hardened and are ready for the bright sunlight and wind.
Eclectic gardening style, drawing from 45 years of interest and experience. Mostly plant in raised beds and containers primarily using intensive gardening techniques.