Shadow wrap short rows are my favourite way to knit short rows. They are easy to remember and to work in my opinion. I prefer them because you do not have to do anything special when you resolve your short rows, i.e. continue working in full rows or rounds again. You simply knit or purl them, depending on which side you are working on. Another plus side is that they are fairly unnoticeable in the final fabric. But that’s just me, perhaps you want to try them yourselves first?
The other thing I want to mention before we start is that if you have successfully completed a Fish Lips Kiss heel (a highly popular short row heel for socks), then you already know how to work shadow wrap short rows. You can totally skip this tutorial. ;)
For this type of short row, you produce so-called twin stitches, where two loops originate from one stitch in the row below. They help connecting the row you just worked with the row above.
Introducing a Twin Stitch on the Knit Side
First off, work to the place specified in pattern. In my photo I marked the stitch below the one that would be worked next. This is the one that we will lift onto the needle and knit. 
You insert your right-hand needle into the stitch below from behind and lift it on your left-hand needle.
It should look like this.
Knit that stitch you just placed on your left-hand needle and place the newly formed loop on your left-hand needle again.
You have two loops originating from one stitch.
Now you simply turn your work with yarn in back and start working in the other direction. You will notice the little gap that is a tell-tale sign of a short row. It also helps to count how many short-rows you have already worked on this side of your piece.
Resolving a Twin Stitch on the Knit Side
Knit to your twin stitch.
Just treat those two loops as if they were one and pull your yarn through both legs at once.
This is what your resolved twin stitch should look like. The two loops are hardly noticeable as they sit below your needle.
Introducing a Twin Stitch on the Purl Side
Again, work to the place specified in pattern. I marked the stitch below the stitch that would be next up, because that is the one we are going to work.
Before you can lift the stitch on your left-hand needle, though, you have to slip the next stitch purlwise to your right-hand needle. This is necessary, because you want the extra yarn that you are going to introduce to sit behind your work, on the private side, and not on the public side.
Go into the purl bump with your left-hand needle from below as shown by the arrow.
Lift the stitch up on your right-hand needle.
Slip the newly formed stitch on your left-hand needle.
Then you purl that slipped stitch like you usually would. 
Tada! You have two loops originating from a single stitch, a twin stitch!
Before you can start working in the other direction, slip the twin stitch purlwise and with yarn in front to your left-hand needle.
As before, there is a gap between your twin stitches and the as-of-yet unworked stitches on your needle.
Resolving a Twin Stitch on the Purl Side
Purl to your twin stitch. Remember that it is the stitch before a noticeable gap on your needle.
Treat the two loops as if they were a single stitch and purl them.
On the purl side, you can clearly still see the two loops that sit right under your needle.
For your viewing pleasure, I knit a few more rows to show you what the shadow wraps look like in stockinette fabric. Remember that I only introduced one per side and the fabric is unblocked, so they slant a bit. That is the way it is supposed to be. You want to use short rows to introduce gussets and strips of extra fabric. Moreover, short rows are mainly used near edges and are not as noticeable there.
In this tutorial, I used the nicely twisted Sweet Georgia Yarns Superwash Sport in Lavender (same yarn that was used for the Runlet sweater) and 4mm Knit Pro needles (or Knitter’s Pride in the US, I believe).
Do you have any questions or comments? Feel free to leave a comment on this post! When you are trying this on a swatch, you can try directly poking your right-hand needle through the stitch below and lifting the resulting loop onto your needle. This is the way I make a twin stitch on the knit side, actually. Guess it takes a bit of practise.  If you compare photo five with the third in this section, you might notice that the position of my needles is totally the same. Yes, you can skip the step with slipping the stitch back to your left-hand needle but I would not recommend it if you are trying it for the first time.