Intarsia, as I mentioned in the introductory post, takes its name from the wood inlay technique, where sections of different woods with different natural colors are laid together to form intricate designs. Because it does use discrete blocks of color like this, it's sometimes also known as "colorblock" knitting. Most of the time, intarsia is employed for designs where the blocks of color are relatively large. There's no reason why it can't be used for smaller areas, but as each block does introduce additional ends to weave in, and as smaller designs generally lend themselves well to stranded techniques, the use of intarsia for smaller designs is less common.
Let's first get a conceptual idea of how intarsia works. In intarsia knitting, the blocks are separate pieces of fabric, linked together at the edges. At the top and bottom, the stitches are linked into the rows above and below just as stitches are linked together in horizontal stripes. At the edges, as you go from one color to another, the new color is brought around the strand of the old color. If you were knitting a single-color item flat, at the edge, you have a strand that comes up from one row to the row above; with intarsia, by bringing one color around the other, you cause these edge strands to lock together -- as if they were linking elbows -- and that attaches the two side-by-side pieces of fabric to each other. If this step is omitted, you will have two parallel pieces of fabric with a vertical opening between them.
Moving from theory to practice, let's look at a very simple example, a rectangle of color B in the middle of a swatch of color A. As you move across a row that contains the rectangle, you will have some stitches of color A, then some of color B, and then some more of color A. Because you're using color A twice on the row, you will need to have two separate strands of color A as you work this row. This requirement is probably the most confusing part of intarsia for new knitters, because it's often not explicitly stated in instructions, so let me make it clear: you will need one strand of each color for each time it's used on a given row. There are some slight exceptions to this -- for instance, if you have just a few stitches of interruption between blocks of the same color, it's common to strand the background color behind the interrupting color for that small area -- but as a general rule, one strand per time used. Therefore, here we have 2 strands of A and 1 of B. Starting on a RS row, you would knit all the stitches of the first block of color A (which I'm going to call A1). Next, you would drop strand A1, then pick up strand B so that it's coming from below and to the right of strand A1. Knit all the stitches of color B, and then drop strand B and pick up the second strand of A (A2), again from below and to the right of strand B. By picking up the strands in this way, you will cause them to wrap around the strand used to knit the prior block; this is half of the locking-together. After knitting all the stitches of color block A2, turn and purl back across this block. Drop strand A2, and pick up strand B, once again from below and to the right, so that it wraps around strand A2. Purl across block B, switch to A1, and finish the row. You now have, on row 1, strand B wrapped around A1, and strand A2 wrapped around strand B, and on row 2, strand B wrapped around A2 and strand A1 wrapped around B, and these two rows are completely locked together. You may have some slight holes at the changes on the first row; this is a normal result of the yarn dangling free at that end, and can be eliminated by drawing the yarn tight before weaving in your ends.
Let's take a look at yarn management; as you might imagine from all the strands and all the crossings, it's a significant issue with intarsia. There are two aspects to this: keeping your strands from tangling with each other, and then keeping your individual strands under control.
My preferred technique for keeping the strands from tangling with each other is to ignore this for the first row; simply bring them across as described above, and then turn at the end of the row. On the second row, bring them back across, and then turn the other way -- in other words, if you turned clockwise from Row 1 to Row 2, turn counterclockwise from Row 2 to Row 3. If you've simply crossed each successive strand across its neighbor on each row, they will automatically untangle as you complete this second turn.
That method does, however, require you to be tolerant of a certain amount of chaos in the middle of the process, and if you're interrupted before you complete the second row and the second turn, you may have some untangling to do. If that's an issue for you, you may want to give Alison's "bobbin walk" method (scroll down to the second half of the page) a try. This method will keep everything neatly under control as you go, but it does require you to knit at a table or other flat surface where your yarn can rest. You'll have to determine for yourself whether you prefer more flexibility or more control.
For managing the individual strands, many people like to wind their yarn up in a little ball of some type, often around a holder, which is called a bobbin. In Alison's pictures linked above, you can see that she uses the EZ-Bob bobbins, and these are pretty neat if you like bobbins at all; they flip open to wind the yarn on, flip closed to hold it, and stack up and snap together when you're putting your project away so you can keep the strands in order very nicely. There are a variety of bobbins out there besides these, though, and essentially they all amount to something smallish to wind the yarn around, and a way to keep it from immediately unwinding itself; if you like bobbins but don't want to buy equipment, you can cut strips of cardboard, with a slit to tuck the yarn into so it doesn't unwind if you drop the bobbin.
Not everybody likes bobbins; they do add some extra weight to the strands, and make the bundle of yarn bulkier than it would otherwise be, which increases the likelihood of catching on other bundles. If you don't want to use them, try making "butterflies": wind the yarn in a little figure-8 around your thumb and forefinger, and then use the end to tie it at the cross point. This gives you a little bundle that will pull from its own center; eventually it'll collapse as you pull the middle out, but you can easily wind it again.
For some projects, you may not want to wind the yarn up at all. For small areas, or if you're using a feltable yarn that lends itself to easy splicing, you can simply use strands of a couple of yards each, and let them dangle; when you need more, simply splice it on. This is the method that Kaffe Fassett reportedly uses for his spectacular multicolor designs, to avoid having a forest of bobbins. This method also makes untangling the easiest, since individual straight strands will pull through each other without catching as bobbins or butterflies would.
Finally, how do you know how long to make the individual strands? Start by counting the stitches in each block of color. A single knit stitch uses about as much yarn as wrapping the yarn around the needle one time. Therefore, you can estimate the length of your strands by wrapping the yarn loosely around the needle as many times as you'll have stitches; if you have a large number, do some fraction of that number as wraps, and then multiply the length of the yarn -- for instance, if you have a hundred stitches, wrap the yarn 20 times and then take 5 times the length that gives you. Don't forget to add a bit for each end, so you'll have some length to weave in, and you may want to add an extra 10% or so just as a fudge factor, to be on the safe side.
That's quite a lot of information for one post, and intarsia in the round is a sufficiently complex subject that I think it deserves a post of its own, so I'll stop here. Intarsia in the round will be up next, and I promise not as tardy as this post.