Standards, Terms, Abbreviations
Yarn Over (yo) is the standard term (at least in the US) for the standard way to wind the yarn around the hook while crocheting all stitches. Wind the yarn up behind the crochet hook and over the top to catch it in the hook. It's also called things like yarn round hook and wool over hook, usually in the UK (yrh, woh, wrh, yoh).
Yarn over(s) also refers to alternatives, as in "mixed yarn overs" or "nonstandard yarn over". The logical opposite of a yo is to wind the yarn around the hook the other direction: up the front of the hook and over the top to the back. It's been called a yarn under (yu). Jane Rimmer likes hook over.
On my shiny new blog I'll add more about yo alternatives, and circling the hook/yarn talk for righties and lefties. And, why I mentioned Jane :)
I've been using only the standard yo my whole crocheting life, and admit to disapproving of the yu a bit. (I'm otherwise not into right vs. wrong rules about crochet!)
Surprise #1: Yes to Yarn Unders Too
Although I continue to uphold the yo as the standard that everyone should learn first and be using by default, an alternative to the yo can also be a great choice! I'd love it if every (intermediate-level) crocheter were empowered with these choices. More about this on the blog.
I've seen the yu and the yarn to front (ytf) conflated in books, so I'm not the only one to have confused these nonstandard ways to begin a stitch. Ytf is also called purlwise and as if to purl. While the yu is pretty common among people doing regular crochet, the ytf option seems to be mostly a Tunisian crochet thing. It's also needed for inverse crocheting.
Surprise #2: YTF is Not a Yarn Over Type
Here's how I straightened them out in my mind: the ytf refers only to where the yarn is just before you insert your hook in a stitch. It's either at the back of your work (the default and standard), or you can bring it to the front. Pin it down with a finger so that it's just below the stitch as you insert the hook into it. THEN you complete the new stitch with yo's (or yu's, or a mixture of the two).
The ytf tempts some crocheters to do a yu because the yarn is already there for it. A yo is usually a better choice though. You need a better reason than convenience to do a yu though! (More on the blog.)