Fair Isle knitting, also known more accurately for most knitters as stranded knitting, is a technique for working two (or more) colors of yarn in the same row. Because the color changes are close together you can simply carry the yarn you aren't knitting with across the back of the work as you go, picking it up when you need it, leaving a strand or float of yarn on the back side of the work.
Fair Isle knitting is pretty easy to do and makes a nice warm fabric because all those floats add extra bulk and warmth. You'll want to hid the back side of the work, but it's a great technique to use for small colorwork patterns on bags, sweaters, socks and other projects where the back side will be hidden.
Stranded knitting is often worked in the round, and it's even easier to do that way than flat, but for the purposes of this tutorial we'll work with a flat swatch and a really basic pattern that I made up as I went along (view the sample Fair Isle chart if you want to follow along).
To begin, simply cast on as you normally would and knit any plain rows called for in the pattern (in this case, four rows of Stockinette Stitch).