When you slip stitch in knitting, you slide the yarn from one needle to the other without knitting or purling. You can either slip stitch as if you were knitting or slip stitch as if you were purling. The difference between the two is where the yarn is placed, either in front or behind the needle. Usually, unless the instructions specify that you are to slip stitch as if knitting, you should assume that you are to slip stitch as if purling.
To slip stitch in knitting as if you were purling, slip the needle on the right into the next stitch on the left needle. Ordinarily, you would purl the stitch at this point. Instead, simply slide the stitch off of the left needle and onto the right. The yarn can be either in front or behind the needle, and either the purl or knit side of the project can face you.
When you need to slip stitch in knitting as if to knit, slide the right needle into the stitch on the left needle. The right needle should go behind the left needle, and the yarn should be behind the needles. Instead of knitting, though, simply slide the stitch from the left to the right.
Slip stitching in knitting as if to purl does not twist the yarn. You won't be able to see the slipped stitch on the knit side of the project. When you slip stitch in knitting as if to knit, you do twist the yarn when sliding the right needle behind the left.
You use a slip stitch in knitting when decreasing stitches. For example, if you are knitting a hat that is pointy at one end and wide at the other, you would slip stitch to decrease the number of stitches in each row as you went up. You can also use slip stitch when knitting a two-colored garment, which is known as mosaic knitting.
Mosaic knitting creates a sweater or other knitted project with a geometric pattern. You fill in the blanks left by the slip stitch with the second color. The benefit of mosaic knitting is that you don't need to work from two skeins of yarn at a time. A disadvantage is that you are limited to only a few stitches of the second color at a time, as the garment will lose shape if you slip stitch more than a few times in a row.
