I have taught more classes on "Two-Handed Stranded Colorwork" than on any other kind of knitting. As I mentioned in my preface post, most stranded colorwork (also referred to by some as "Fair Isle") involves working rows with two, and no more than two, colors at a time. The non-active color is carried along behind the work until it is used again.
It is quite possible to knit a stranded colorwork project using only the one hand that you normally use to carry your knitting yarn -- you would have to drop one color and pick up the other each time the color changes. After a while, you might come up with a way to hold both yarns in the same hand (I did this when I was young knitter), but it does get complicated when there are long stretches of one of the colors, and you have to drop both yarns to wrap one around the other. It is very easy to have your yarns get tangled together.
This is why most stranded colorwork knitters eventually learn a two handed approach.
PART 1 -- YOU ALREADY KNOW ONE OF THESE TWO THINGS VERY WELL.
Holding the light and dark colored yarns with my right and left hands, allows me to knit the light color stitches with my right hand (using what is called the English method).
And knit the dark colored stitches with my left hand (which is called the continental method).
One of these methods is actually the way that you normally knit now. The other is one that you may need to practice a bit. I recommend that you work a swatch knitting with the opposite hand from that which you normally use, and then use both hands together for a fairly simple colorwork pattern like the herringbone section of my Equilibrium cowl.
When knitting this herringbone pattern, the longest number of stitches in one color is three. The unused color is carried along as a "float" behind the active knitting color. It is fairly easy to mange these relatively short floats.
1) Always carry the unused color loosely in the back. Though it is possible after knitting to tighten an overly loose float, it is truly impossible to fix floats that are too tight. They can cause puckering on the right side. I pause briefly (mindlessly, and almost instinctively) after every few stitches to actually spread the most recently knit stitches out a bit on my right needle... this stretches out any floats behind them to an appropriate length. Practice this in the beginning; and you will find that before too long, you hardly have to think about it.
2) When working two-handed stranded colorwork, try placing the ball of yarn that you are working with your right hand to your right. And place the ball of yarn to your left that you are using with your left hand. Surprisingly, even when you do need to use the methods that I will describe below to twist the strands together, the two yarns will never tangle.
3) Stranded colorwork is best worked in the round.
PART 2 -- TWO MORE TECHNIQUES TO LEARN AND YOU WILL HAVE MASTERED TWO-HANDED STRANDED COLORWORK.
When you work a design where there are more than three or four stitches in one color -- where the floats would be an inch or more long -- you can use the next two techniques to "catch" or "trap" or "wrap" or "weave" your floats. I have heard each of these terms used. The methods themselves are fairly easy, you can learn them in no time with a bit of practice.
Hold the work and two strands of yarn as you practiced above. Notice that for each of the following, the first step is always to stick the right needle tip into the stitch to be worked.
To trap the color held by the LEFT HAND when you have an inch or more of stitches in the color worked with the RIGHT HAND:
A. Stick the right needle tip into the next stitch to be worked. Then lay the yarn being held with your left hand across the top of the right needle tip, so that it lays between the needles.
B. Now wrap the yarn in your right hand around the right needle tip as you normally would do when knitting with your right hand.
C. Then complete the knitted stitch. Note: the actual "trapping" actually happens when you knit the next stitch with the right hand.
To trap the color held by the RIGHT HAND when you have an inch or more of stitches in the color worked with the LEFT HAND:
A. Stick the right needle tip into the next stitch to be worked. Next take the color in your right hand and wrap it around the right needle tip as you would if you were to "pretend knit" with it.
B. Next wrap or "pick" the yarn in your left hand as you normally would to knit with it, but do not complete the stitch.
C. I usually call the next step "un-pretend" to knit with the color in your right hand. Simply unwrap it from the right hand needle tip. It will go around and back.
D. Complete the knitted stitch. Note: the actual "trapping" actually happens when you knit the next stitch with the left hand.
In the split chevron portion of my "Equilibrium" cowl, I would catch the opposite color yarn in the middle of any group of 5 or 6 stitches.
4) Avoid trapping a yarn when working a stitch directly above a stitch where you trapped the same color yarn in the row below. Trap it a stitch before or a stitch after. (Otherwise you will get what looks like a vertical float over two rows.)
5) Do not try to trap a color with the very last stitch knit with the other color. You do need to work at least one more ordinary stitch to actually complete the "trapping".
Tutorials such as this one have a lot of technical details. I hope that these techniques will help you with your stranded colorwork projects, but do give your self plenty of time to learn them. Enjoy your colors along the way!