What is the slash command to speak in General chat on Diablo 3?
It's /c (for channel)
/c Hello there.
This, of course, requires you to actually be in the General channel. If you joined another channel the same command would let you speak there, and if you're not in a channel the command wouldn't work.
You can also press the Quick Chat button next to the chat box, or just hit the [tab] key with chat open, to choose where your messages will be sent.
Blizz provided a helpful tutorial on joining chat channels here as part of a bug workaround. The relevant portion of which is this :
Do note that as of patch v1.03 (v.18.104.22.16857), chat settings are saved when you log out, so if you join General and log out, you'll re-join General the next time you log in.
Chat settings and preferences will now be saved whenever you log out