If you are familiar with stranded knitting (of which Fair Isle is a subset), you know that you carry two or more yarns and pick which one you want according to a charted design. Each yarn gets used for stitches. In inlay knitting, only the background yarn is knit; the other yarn(s) are held in front of or behind the background stitches as they are being made. In effect, it is a type of embellishment that you do at the same time as the actual knitting. The accent yarn is not used up at the same rate as the background yarn and it does not have to be pulled through other stitches. This makes it an ideal technique for getting the most out of expensive, eccentric, or delicate yarn. Also, even in plain yarns you get a pretty neat textural effect.
I always carry my knitting yarn in my right hand so I held the inlay yarn in my left. Then it was just a matter of bringing it forward and bringing it back. I did find it a bit easier to use the right needle to help push the inlay yarn into position rather than depending on my left hand alone.
For the pink and purple swatch, I just grabbed whatever was in the bottom of my knitting basket and worked a typical under and over pattern. I later read (in The Principles of Knitting by June Hemmons Hiatt) that the inlay yarn should be locked into the selvedge stitches. Since I hadn't done that on the first swatch, I didn't do it on the white and pink one either. You can see how the knitting pulls where the inlay yarn is carried up from row to row. It's not particularly bad and I do suspect that picking up stitches along the edges would hide the problem nicely.
But there is another reason to keep the inlay yarn out of the selvedge stitches: unlike plain stockinette, the side edges of inlay knitting come out perfectly flat. A narrow edging would be adequate in this situation and that should have some decorative potential. Unfortunately, the top and bottom edges do curl as in normal stockinette so they will need a more standard treatment.