I do use the two-handed method and frankly, I adore it. I actually pout a bit if I have to knit some ribbing or a stripe with just one hand. So I do want to urge all new color knitters to try using two hands on a small project. It only took me one sock project to fall in love with this method and the feeling of flow when using two hands.
To me the benefits of two-handed knitting are the relief the dominant hand gets and the sheer speed. It is much faster for me because I can start one of my hands knitting with the second color before I'm even done knitting with the first color with the other hand. I hold the right hand needle like a pencil but for some reason I don't with the left hand needle.
I tension the yarns through my fingers as shown although the yarn is too low on my left hand in this photo. When knitting I keep the yarns above my middle knuckles. The yarn in my right hand will be the background color and the yarn in my left hand will be the dominant color. In Carol Rasmussen Noble's Fair Isle mitten book, she says the stitches made by the left hand will be slightly larger if you're normally an English/American knitter and after looking closely at my knitting, she is definitely right in my case.
My method of weaving the yarns through my fingers is a pain if you need to get up frequently while knitting but I have at least learned how to keep the yarns woven through my fingers like that while changing from one dpn to the next.
To knit the left hand yarn, you knit Continental and either grab the yarn by going over or under the yarn. I go over.
When I need more yarn I simply lift my index fingers like this and pull more yarn out from the skein.
To knit with the right hand yarn I simply knit English/American and wind the yarn around the right-hand needle.