I feel much more confident giving my hand knit items as gifts now that I know a better method for weaving in yarn tails. Ideally, you want yarn tails to be secure, yet invisible. You also want to avoid affecting the stretch of the fabric with your yarn tails. Following, is the method I use for weaving in yarn tails in garter stitch. I used a red yarn tail for illustration purposes.
On the wrong side of the fabric, find a purl bump. Bring your yarn tail through the hole on the right side of the purl bump. The needle is under the purl bump in this picture just to illustrate the bump I am talking about.
The final result, is two sets of purl ridges that lie on top of purl ridges that are already there. Therefore, the stitches are hidden and should have minimal effect on the stretch of the fabric since they follow stitches that are already present.