Here are Helgi's Mittens from Nancy Bush's Folk Knitting in Estonia. My gauge was way off so these are child's mittens instead of women's size. Fortunately I have a lot of young girls on my gift list. I used size 1 dpns and Nature Spun Fingering Weight yarn. I changed the thumb pattern.
I was playing around with different ways to knit with these mittens. I think if you're a one-handed stranded knitter then knitting Continental is pretty easy. You simply strand the first yarn around your left index finger and the second yarn around your left middle finger. Then you simply pick whichever yarn you need as you're knitting.
You can also use a strickfingerhut or knitting thimble for knitting this way. The strickfingerhut helps you hold the yarns more tautly to make picking easier.
Right handed knitting with only one hand is more complicated. To do it I put the first yarn over my index finger and under my middle finger and over my ring finger. The second yarn goes under my index finger, over my middle finger, under my ring finger and over my pinky. Stranding the yarns over two fingers allows you to tension a bit better. To knit either use your index finger to throw the yarn around the needle or your middle finger depending on which yarn you need for that stitch.
No matter what method you choose it is going to involve a bit of re-training your fingers and feeling a bit awkward at first. When I taught myself two-handed knitting I picked a small project and did it entirely that way. By the time I finished I felt comfortable with the new method.