There are lots of different ways to do short rows. I have unvented my own favorite way, and I wouldn't be at all surprised if I'm not the only one. But because I haven't found this particular method documented online anywhere, here is a photo tutorial. This tutorial shows how I work over a single short row on the RS and the WS of the fabric. Mitered short row heels and toes are out of scope for this post.
First, here is one short summary of some classic methods. My method is closest to the "catch" method illustrated here. Run a Google search and you will find many more articles.
Also, the dear departed incomparable Cat Bordhi came up with her own method of working short rows as part of her Sweet Tomato Heels shaping. This is fairly new and so not included in most short row summaries you'll find online. My method is also similar to Cat's. Watch her STH video and right after 6 minutes is when she begins to show the details of how she closes her short row gaps.
Alright. So here's how I do it.
In the sample below, the short rows are worked in red, and the last full row just below them is in yellow. This should hopefully help you to see how the sts are related to each other. Note how the last red stitch is worked only once; that's because when you turn the work to the WS, you slip the first stitch.
Here's how the other side looks from the WS.
I'm using a third color (blue) to distinguish the row where the gap between the last red stitch and the first yellow stitch is closed. On this row, knit all the way up to the last red stitch -- the one to the immediate R of the gap.
Insert the tip of the L needle into the back of the first yellow stitch on the R needle, 2 sts below the one you just knitted. As you do this, you should feel the stitch to the L tighten up a little. That's because they are right next to each other on the same row.
The gap is now closed, and completely invisible.
Now on to the other side. Working a short row conceal from the WS is a pain. I personally prefer to knit left to right with the RS facing me rather than purl on the WS, but since this is not how most knitters work, here are the instructions for doing my short row method from the WS.
Just as you did when working on the RS, work (in this case purl) up to the last short row (red) stitch.