What is singular "they"?

Sometimes it's useful to be able to talk about someone without specifying their gender. Maybe they're an underspecified hypothetical person who could turn out to be either gender ("the applicant"), maybe their gender is irrelevant ("my lab partner"), or maybe they don't have one ("my friend Alex"). In these cases you can use "they" to refer to just one person, even though "they" is more commonly used for multiple people: "the candidate seated themself by the window".

That's ungrammatical! You can't do that!

What's grammatical changes over time. The phrasing "you can't do that" uses "you" in the singular, which was once just as ungrammatical. A few hundred years ago you/ye was strictly plural, while thou/thee was the singular. Over time you/ye expanded into the singular as a way of indicating respect and deference, and eventually came to be used in all situations.

Hmph. I won't use singular "you" then either.

You might get along well with this guy.

In the singular is it "they is" or "they are"? What about "themself"?

Always "they are". It's just like "you": "you are," not "you is," even for just one person. Similarly, it's "themself" for one, "themselves" for more than one. Again it's just like "you": you would say "yourself" for one person, "yourselves" for multiple.

Why are some uses ok, and others ugly?

Hearing "when the next person walks through that door I'm going to jump out and surprise them; 'boo!'" most people don't feel weird about the "them," while in "my dad says they're going to cook dinner tonight" most people are looking around trying to figure out who the "they" is that's going to be cooking. In general, when talking about a specific person ("my kid") or when gender is known ("a boyfriend") people are less ok with it, and when you have both together ("my boyfriend") it's too much for most people. There's a spectrum of acceptance here, and most people are somewhere in the middle.

I like singular "they"; how can I help it grow?

Use it in situations where it's useful. One thing pushing us toward full acceptance of singular "they" is social networks using it for people who haven't specified (or have hidden) their gender. So you see "Mark updated their profile picture" a lot and it becomes less weird feeling. I want singular "they" so I can write things like "the user won't know where to look for their server configuration" in design documents at work, and luckily I don't have to wait. I just use it like I want it to be used.

Other ideas: Pushing They.

Wouldn't this just get super confusing?

When you see a sentence like "John told Sarah they were angry" you can see it would be less ambigous as 'he' or 'she'. By giving up gender matching we do lose one of the hints we use to figure out what a pronoun is referring back to. Now, if the sentence had been "John told Samuel he was angry," we'd have the same problem, but a decent fraction of the time gendered pronouns increase clarity. It turns out, though, that many languages do fine without gendered pronouns. For example, in Chinese you say 'ta' where in English you'd say 'he', 'she', 'it', or (singular) 'they', and it all works fine. We know this won't cause a mess in English because it's not a problem in other languages.