"Intarsia" is color knitting comprised of large areas of color. This Stars + Stripes Felted Hot Pad is a typical example of intarsia knitting:

The truck in this pattern from Roo Designs is another good example:

Some Basic Rules

Intarsia knitting isn't hard, but there are some basic rules to know.

Unlike fair isle knitting, the yarn is not stranded across the back of the work in intarsia knitting. Instead, you have a separate ball of yarn for each area of color. If you have a lot of color changes in one row, you may want to wind the separate colors onto bobbins to help you stay organized. 

The other important rule to keep in mind is that when you switch from one color to the other you have to "twist" the yarns in order to avoid holes. I like to think of it as "trapping" the yarn, because you put the yarn you're finished using in front of the new yarn, trapping it between the new yarn and the knitting. This manoeuvre is always done on the wrong side of the work.

Here are all the scenarios you will encounter knitting intarsia:

Vertical Lines

The red lines in this picture show color changes that form vertical lines:

When the color change forms a vertical line, knit to the change, bring the old yarn in front of the new yarn (again, on the wrong side of the work), and knit the new color stitch.

Here is what that looks like when you're knitting a right side row:

And here it is purling a wrong side row:

Diagonal Color Changes

When the color design is at a diagonal, twisting depends on if the design is slanting to the right or to the left. If it is slanting to the RIGHT as you're looking at it, you need to twist the yarns, regardless of whether you're on the knit or the purl side of the piece.

The moments marked in red are right slants on the knit side:

The twist in that case would look like this:

On the purl side, the right slant color changes happen along this red line and also require a twist: 

The twist on the purl side looks like this:

If the design is slanting to the LEFT, like this: 

Or like this:

You don't need to twist the yarns at all. You can just drop the old yarn and start knitting or purling with the new yarn.

If you find this right versus left slant confusing (sometimes I do!), it's fine to just always twist the yarns. When in doubt, twist!