Every single knitting project involves finding something to do with yarn tails. Even the smallest project that only uses one ball of yarn leaves a tail at both ends from casting on and binding off. With larger projects, every new ball of yarn or [heaven forbid] knot in the middle of a ball leaves two new ends to deal with. Add in color changes and fiddly bits like neck shaping and sock heels and any one project can have a dozen little pieces floating around on the wrong side. What shall we do?

When I first started knitting and was ready to "weave in all ends", I threaded my trusty yarn needle and, catching a few purl bumps, ran the yarn end across the wrong side on a diagonal. Problem was that diagonal line wound up showing through on the right side a little too often -- not a pretty sight.

Fortunately I came across an article in Cast On magazine in the spring of 2003 about using a duplicate stitch on the wrong side to weave in yarn ends and had a "aha!" moment. It's a marvelous way to deal with this universal dilemma -- the yarn end is nearly invisible on the right side of the work and, just as importantly, stays where you put it, proving once again that you're the one in charge of your knitting.

First let me just say a few words about what to do when you come to the end of one ball of yarn and are going to start working with the next. What I do -- and this under the influence of Elizabeth Zimmerman in Knitting Without Tears -- is work the next stitch with both the old yarn and the new, held together, leaving a 5-6 inch tail of both yarn ends dangling.

On the next row, be very sure to treat these two strands of yarn as one stitch. No knots necessary and a good thing, too, since everything out there says to avoid them like the plague. Knots have a terrible tendency to pop through to the right side of the work when you're least expecting it or leave an unseemly, not to mention uncomfortable, lump. I have yet to be troubled by a hole this way, especially when the left over ends are secured as securely as we're about to secure them.

But before the leave the subject of knots...when you come across one in the middle of a ball of yarn (and is there anything more annoying?) untie it or cut it out and treat the join as a new ball of yarn. You'll be glad you did.

Now, moving on to securely securing those yarn ends. First of all be sure you've got a proper yarn needle, one with a large eye and a not-too-sharp end as you don't want to split the yarn as you weave in ends. Have a nice sharp pair of scissors on hand and a good light source so you can see what's going on. Take a good hard look at the "wrong" side of your knitting, or, if it's reversible, figure out which side you want to hide the end on. Follow the yarn horizontally across one row, noticing where the yarn travels and how it connects to the rows above and below. This is your guide for where to make the yarn end travel. The wrong side of stockinette stitch is the most straightforward for this type of duplicate stitching (or at least it is for me) so let's start with...

Reverse Stockinette

(By the way, the "yarn end" has been digitally drawn onto this and some of the following images to more clearly illustrate the path of the yarn.)

Thread the yarn end onto your needle and guide it through the purl bumps as shown, trying to match the tension of the knitting as closely as possible. I'm having a hard time trying to come up with a way to describe this in writing except to say that going through two purl bumps at a time you'll be inserting the needle on the diagonal first one way and then the other. Do this for a couple of inches or so and you'll have one seriously secure piece of yarn -- in fact, I had a hard time removing the ends from my sample pieces when I was practicing. Cut the remaining end with your scissors, leaving a short tail on the wrong side. If it's a particularly slippery yarn end you might want to double back through the last two purl bumps and leave a slightly longer tail.

Stockinette

The principle for stockinette stitch is exactly the same -- following the path the yarn takes across the row -- but instead of inserting the needle into the bumps of purl stitches, you'll be inserting the needle under the lower part of the V created by the knit stitch on the row above...

and the inverted V of two adjacent stitches on the row below.

Again be sure to adjust the tension of the duplicate stitching to the tension of the knitting. The closer you get, the more invisible the weaving becomes.

Garter Stitch

Garter stitch is a bit trickier than it would seem to be at first glance. When the finished object is meant to be reversible, such as a scarf or a dishcloth, there is no "wrong side" in which to hide the yarn ends so you'll have to just pick a side at random. Fortunately using this method means the ends behave themselves very well and won't be waving their little arms at innocent passers-by.

Look at your garter stitch carefully. When it's just laying there, it looks quite a bit like reverse stockinette stitch, with purl bumps waiting around to be used. And I must admit that sometimes I treat garter stitch as reverse stockinette stitch and simply weave the ends through those purl bumps... one can't be a perfectionist all the time. But we all know that garter stitch isn't the same as reverse stockinette stitch. Looking at garter stitch from one side, stretched a bit so the rows are spread apart, it reveals itself to be one row of knitted Vs alternated with one row of purl bumps.  

That means you'll be catching one purl bump (as for reverse stockinette) and then going through one V (as for stockinette stitch) for each stitch across the row. If you're having trouble "seeing" the stitches, try pulling the rows apart a bit by stretching it over your index finger.

As a final note, it must be said that this method works best with yarn that's worsted weight or thinner. If you're working with a thick yarn, duplicate stitch will add too much bulk and show itself. If that's the case try this: split each yarn tail in two and pull it gently apart to the point from which it emerges from the work. Release it and let it relax so some of the excess twist comes out then weave each in separately, moving to one row above or below for the two extra ends.

References:
Knitting Without Tears by Elizabeth Zimmerman
Those pesky yarn tails by Arenda Holladay. Cast On magazine, spring 2003.