Intarsia is a method of colorwork in knitting and crochet. It's also a kind of mosaic woodworking, but I know next to nothing about woodworking so I'll stick with the textile aspect. Most of this is knitting-centric, although crochet overlaps. For the most part, crocheting an intarsia pattern is simpler.
If you've ever been given a hideous sweater with say a large black scottie dog worked on a red background, then you've likely been a victim of cruely misapplied intarsia. Still, intarsia can also be used to make insanely gorgeous pieces or fun pieces to satisfy the inner geek. It is not the fault of the technique, after all.
Essentially, intarsia is a way of working medium to large areas of color. It can be used to reproduce a picture or create stripes or geometric forms in the fabric. The very simplest form of intarsia is horizontal stripes spanning the entire width of the fabric.
------------ 9
------------ 8
------------ 7
MMMMMMMMMMMM 6
MMMMMMMMMMMM 5
MMMMMMMMMMMM 4
------------ 3
------------ 2
------------ 1
In such stripes, there's no secret technique. When it comes time to work the new color, one simply works with the new color instead of the old. It's that simple.
Vertical stripes are the next step up. They're a little more effort, even if they don't look it to the uninitiated. My favorite application for this technique is placing a contrast color cable on a dark background. This is also the technique to use for cables with the "legs" in different colors. This creates a barbershop pole twisting color effect in the most basic of cables, but can be used for much more intricate designs and patterning.
--MM--MM--MM 9 ←
--MM--MM--MM 8 →
--MM--MM--MM 7 ←
--MM--MM--MM 6 →
--MM--MM--MM 5 ←
--MM--MM--MM 4 →
--MM--MM--MM 3 ←
--MM--MM--MM 2 →
--MM--MM--MM 1 ←
Knitting is worked from the bottom up and each row is worked right to left. If one knits a flat piece, it gets turned at the end of a row and one goes back in the opposite direction. This zigzag is the most basic configuration of any piece of flat knitting, uncomplicated by increasing, decreasing or short rows.
The problem of working vertical stripes should become evident if you consider the first row. If one starts with black (M) and switches to white (-) one either has to strand the black behind the white to have it available to work the next two stitches or the stripe has to have its own ball of yarn. Now, stranding is a good method of doing color work. It's the basis of an entire technique called, unsurprisingly, stranded color work. Fair Isle knitting is one of the most famous traditions within stranded color work, and Icelandic sweaters are also famous for their two color patterns. Still, stranding for vertical stripes is not a good idea when the stripes are wider than two or three stitches. Stranding starts doing things to one's tension and can cause the fabric to pucker or the stitches to be loose, and it also reduces the flexibility of the finished fabric. There is a risk of long floats in back catching on things, as well. And stranding can use more yarn as an extra layer of strands builds up behind the fabric, and because of this the resulting fabric is also thicker.
Stranding also is not suitable for very large areas of a single color within a sea of another color. Yarn really shouldn't be stranded more than a few stitches. Some traditions object to stranding it further than 4 stitches with rare exceptions, others cite 7 as the best number. Stranded colorwork is most commonly used for two colors per line in a relatively small, often (but not necessarily) repeating all-over pattern such as this:
O--O-OOOOO-O--O--O-OOOOO-O--O--O-OOOOO-O-- 13
--OO--OOO--OO---OO--OOO--OO---OO--OOO--OO- 12
-OOO---O---OOO-OOO---O---OOO-OOO---O---OOO 11
-MMM--M-M--MMM-MMM--M-M--MMM-MMM--M-M--MMM 10
-MM--MM-MM--MM-MM--MM-MM--MM-MM--MM-MM--MM 9
-M--MMM-MMM--M-M--MMM-MMM--M-M--MMM-MMM--M 8
MOOOOOOMOOOOOOMOOOOOOMOOOOOOMOOOOOOMOOOOOO 7
-M--MMM-MMM--M-M--MMM-MMM--M-M--MMM-MMM--M 6
-MM--MM-MM--MM-MM--MM-MM--MM-MM--MM-MM--MM 5
-MMM--M-M--MMM-MMM--M-M--MMM-MMM--M-M--MMM 4
-OOO---O---OOO-OOO---O---OOO-OOO---O---OOO 3
--OO--OOO--OO---OO--OOO--OO---OO--OOO--OO- 2
O--O-OOOOO-O--O--O-OOOOO-O--O--O-OOOOO-O-- 1
Clearly this sort of pattern is much too much trouble to work in intarsia. The sections of color are too small, and it would require days just to weave in all the ends for all those little sections. Stranding in this case would save time and yarn.
However, if one has a large motif to go on a garment and it's worked in patches of several colors the drawbacks of stranded color work outweigh its benefits. In cases like this, intarsia is much more efficient and effective. The caveat to this is that intarsia cannot be done in the round, again because of where the yarn has to be when you get to the block of color.
Properly done intarsia doesn't warp the fabric at all. Each section of color has its own ball of yarn and the colors interlock on the back of the piece.
So you're ready to start working a design in intarsia. Let's revisit the scotty dog idea since it's likely to have good, strong contrast which shows up better in ascii art. Below is a mocked up version of a chart with 3 colors; the background, the dog itself, and the bow around its neck.. The chart is a necessary part of any intarsia pattern more complicated than stripes and this is as close as ascii art can get to what they look like. Many intarsia charts are worked up with the cells colored in, but the cells are always clearly marked to make counting stitches easy.
------------------------------------------- 24
------------------------------------------- 23
-------------MMM--------------------------- 22
------------MMMM--------------------------- 21
-------MMMMMMMMMM-------------------------- 20
------MMMMMMMMMMMM------------------------- 19
----MMMMMMMMMMMMMMMPP-----------------M---- 18
--MMMMMMMMMMMMMMMMPPPP----------------MM--- 17
--MMMMMMMMMMMMMMMPPPPPM--------------MMM--- 16
---MMMMMMMMMMMMPPPPPMMMMMMMMMMMMMMMMMMMM--- 15
----MMMMMMMPPPPPPPPPPPMMMMMMMMMMMMMMMMM---- 14
----MM---PPPPPPMPPPPPMMMMMMMMMMMMMMMMMMM--- 13
---------PPPPPMMPPPMMMMMMMMMMMMMMMMMMMMMM-- 12
----------MMMMMMMMMMMMMMMMMMMMMMMMMMMMMM--- 11
----------MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM-- 10
----------MMMMMMMMMMMMMMMMMMMMMMMMMMMMMM--- 9
----------MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM-- 8
----------MMMMMMMMMMMMMMMMMMMMMMMMMMMMM---- 7
----------MMMMMMMMMMMMMMMMMMMMMMMMMMMMM---- 6
----------MMMMMMMMM--MM-MMM---MMMMMMMMM---- 5
----------MMMMMMMMM------------MMMMMMMMM--- 4
---------MMMMMMMMMM-----------MMMMMMMMMM--- 3
------------------------------------------- 2
------------------------------------------- 1
Charts are representations of the work looking at it from the front. Now, assuming row 1 is knit across starting from the right and going left, it's clear stranding won't work here. There are just too many wide stretches. And intarsia ideally doesn't use stranding except in very very rare circumstances. To show one way this piece could be worked, I've modified the chart a little.
------------------------------------------- 24 →
------------------------------------------- 23 ←
-------------MMM--------------------------- 22 →
------------MMMM--------------------------- 21 ←
-------MMMMMMMMMM-------------------------- 20 →
------MMMMMMMMMMMM------------------------- 19 ←
----MMMMMMMMMMMMMMMPP-----------------m---- 18 →
--MMMMMMMMMMMMMMMMPPPP----------------mm--- 17 ←
--MMMMMMMMMMMMMMMPPPPPM:-------------mmm--- 16 →
---MMMMMMMMMMMMPPPPPMMMMMMMMMMMMMMMMMMMM--- 15 ←
----nMMMMMMPPPPPPPPPPPMMMMMMMMMMMMMMMMM---- 14 →
----mm---PPPPPPmPPPPPMMMMMMMMMMMMMMMMMMM--- 13 ←
---------pPPPPmmPPPnMMMMMMMMMMMMMMMMMMMMM-- 12 →
----------MMMMMMMMMMMMMMMMMMMMMMMMMMMMMM--- 11 ←
----------MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM-- 10 →
----------MMMMMMMMMMMMMMMMMMMMMMMMMMMMMM--- 9 ←
----------MMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM-- 8 →
----------MMMMMMMMMMMMMMMMMMMMMMMMMMMMM---- 7 ←
----------MMMMMMMMMMMMMMMMMMMMMMMMMMMMM---- 6 →
----------MMMMMMMMM--mm-mmm---MMMMMMMMM---- 5 ←
----------MMMMMMMMM------------MMMMMMMMM--- 4 →
---------MMMMMMMMMn----------:MMMMMMMMMn--- 3 ←
------------------------------------------- 2 →
------------------------------------------: 1 ←
In the main contrast color, n indicates where a new strand is added; m indicates where duplicate stitch can be used to add a stitch or two rather than starting a new strand. ":" indicates where a new strand is added for the main color and p indicates a new strand of the secondary contrast color. I haven't indicated where strands would stop being used as that should be fairly self evident, and I've made liberal use of duplicate stitch to keep the chart simple. Charts normally don't indicate when to change color as it is up to the knitter or crocheter to decide how they want to structure the piece.
Now, one thing a knitter must do is make sure that the yarn strands interlock between colors or else there will be vertical slits between the colors where one ends and the other begins. This can be a desireable design feature in some cases, but usually it's just wrong. It is a simple matter of twisting the two strands once before working with the new color. This, unfortunately, will cause the strands to start tangling. Depending on the number of colors, this can be very, very annoying. This is one reason to wind small butterflies or bobbins of yarn, just enough for each section, which hang off the back of the work. These small bobbins tend to untangle more easily than loooooong strands attached to distant balls of yarn. However, these small bobbins also tend to be wasteful and I only use them when I have more than 6 or so strands in play. In order to control the tangling, I usually twist all the colors in one direction across the front, and then in the opposite direction across the back. Also, when I turn the fabric, I make sure I'm not wrapping all the strands around each other in one massive twist. This small amount of care makes dealing with many balls of yarn much easier.
In knitting, these kinds of motifs are almost always worked over stockinette as the purl side of stitches will show the color change. Texture stitches can be used, however, as long as stitches which transition between colors on a new row are always knit (when seen from the front). This keeps the color changes sharp.
After the piece is completed, all the ends of the yarn hanging off the back need to be woven in back along their own color lest they unravel. Sometimes embroidery is worked over the finished motif to outline sections and otherwise make it more obviously a picture of whatever is being represented. I've seen very impressive intarsia trees with different things embroidered on them to represent winter, spring, summer, and autumn for instance. However, in the case of this scotty dog, at most the bow around the neck would be outlined in one of the contrasting colors so it looks less like an undifferentiated blob.
Intarsia in the round: Yes, I know I said it's not possible, and it's not. However, there is a technique which allows you to join the edges of the piece while working it. It lies a flatter than a seam would, and is less noticeable as well. It is not invisible however. Essentially, decide which row to start the motif and at the beginning of that row yarn over. Work as charted. The last stitch of the row gets worked together with the yarn over as if working a decrease. I like to work this first yarn over twisted so it is tightly closed. Then, turn the work, yarn over and go back and work a purl side row. Again, work the last stitch together with the yarn over, this time with the yarn over in front (it should always be on the purl side). Continue to yarn over at the beginning of the row and working the last stitch together with the yarn over until the intarsia motif is completed and the piece is on a knit side row. Then continue working in the round.
A note on charts: I've used ascii art to represent the charts here but it is important to remember that in knitting stitches are almost never square. Most stitches, especially in stockinette at a "normal" gauge, are wider than they are tall. This has to be taken into account when designing the chart or else the finished motif will look squat and depending on what is being represented it can look extremely bizarre. The best way to adjust for this skew is to take one's gauge and lay graph paper matching that gauge over the image. I do this in Photoshop Elements by opening a pdf of the graph paper with a transparent background and then copying and pasting it over the image I want. This allows me a great deal of freedom in changing the size of the finished motif. There are many other ways of doing this, however, and many readily available charts are simply drawn over a sort of generic knitters graph paper which is unlikely to match one's gauge exactly, but compensates enough to be recognizable when worked up.
Resources:
Generate actual size and scaled graph paper and save 'em as a pdf: Tata&Tatao
Another site where you can generate your own graph paper, this time as a png: The Knitting Fiend
A site which generates a graph based on your jpeg, gif or png file. I prefer methods which have more control, but it's handy for simple, high contrast images: KnitPro