Multicolor knitting can be as simple as stripes, where we change yarns every few rows. Beyond stripes, there are many techniques: Fairisle, intarsia, two color tuck, knit-weaving and some surface embellishments techniques. The playlist linked above explores the many methods of multi-color knitting on both machines and looms.

In the illustration, the cover of my Suitable for Framing book shows fairisle examples. The green diamond was knitted with intarsia. More about fairisle vs. Intarsia below. The lace trimmed suit in the center uses a surface embellishing technique. The Dream Weaver coat at far left is made by knit weaving. Knit weaving involves carrying a yarn along that gets caught in the stitches but isn't actually knitted, which makes it possible to expand the yarn choices to include yarns that aren't suitable for machine knitting. In two color tuck, illustrated by the blue and brown swatch, one color is knitted at a time but the structure of tuck stitch places them side by side in the fabric.  Being tuck stitch and lacking floats, this fabric comes out much wider than fairisle knitted with the same yarn and on the same machine or loom. The scarf with a heart and the sample below it are examples of intarsia and fairisle on knitting looms. Movies on all of these techniques are included in the playlist, sometimes including a complete free pattern. Links to the books that have the written patterns are given below.

What's the difference between intarsia and fairisle? Both have 2 or more colors of stitches in a row of knitting. In fairisle the strands of yarn are both carried across the knitting. When a stitch is made in one color, the other stays in the back of the fabric until it is called into work somewhere else along the row. This is why fairisle is less stretchy than stockinette. Those strands, called floats, limit the sideways flexibility of the fabric. Fairisle is mostly used for small, repetitive designs and many knitting machines can do it automatically. Intarsia has no floats and is always at least partly arranged by hand. If the machine has an intarsia setting or special carriage, that feature brings the needles to upper working position after knitting a row. The artisan arranges the yarns in the needle hooks as desired, working by hand, then the carriage is used to knit the row. Intarsia is more time consuming but allows for big picture designs. It has no floats.

Links to the pictured patterns are underneath the photo below. Each link takes you to a full description on Ravelry.