This method has a long name that says it all: Knit into the Front and Back, or Kfb. The trick is to do it all in one stitch and keep your tension VERY LOOSE.
Begin by knitting the stitch, with the yarn at the back of the work and the needle going into the stitch from the front.
Stop short of lifting the stitch off of the left needle. Keep the old stitch on the left needle and the new stitch on the right needle.
Give yourself plenty of slack by wiggling the new stitch on the right needle. Insert the right needle behind the left needle into the back of the stitch.
Knit the stitch again by wrapping the yarn around the right needle from back to front as you would normally.
Draw the stitch through and lift both stitches off the left needle.
The increase, shown in stockinette stitch, looks like a small purl nestled between your knit stitches.