Mosaic knitting is actually very simple; all you're doing is slipping stitches in one color while you knit or purl stitches in another color. Unlike traditional stranded knitting, where you're working with two or more yarns at any given time, with mosaic, you're only working with one yarn at a time. In addition to making colorwork simpler to manage, this feature of mosaic knitting means fewer floats and a more flexible fabric.
When working a mosaic pattern, you're essentially working two-row stripes. You work with one color for two rows, knitting or purling all the stitches that will be in the working color (according to your pattern) on both rows and slipping the stitches that will remain in the non-working color, typically with the working yarn held on the wrong side. Then, on the next two rows, you do the same thing — this time knitting or purling certain stitches using the new working color (the color you slipped on the previous two rows) and slipping stitches that will remain in the new non-working color (the one you worked with on the previous rows). Rows are usually worked in Stockinette, Garter, or a mixture of the two.
When slipping stitches, be sure to carry the working yarn loosely on the back of the work (wrong side) so that the fabric has room to stretch naturally when blocked.
Anchoring Long Floats in Mosaic Knitting
Brigit Hampel (enablerqueen on Ravelry) came up with a method for anchoring long floats in mosaic knitting while testing the Chevronelle Wrap. It is worked on the row following the pair of rows with the long float, on the stitch over the center of float to be anchored. Insert your right-hand needle into the next stitch as if to knit, take the tip under the two long floats, catch the working yarn, and complete the knitted stitch.