I see where you can edit a post/thread but I don't see where
you can delete an old post/thread.

You can delete a post, not a thread.

To delete a post, click edit, then "delete message" option.

That's strange. Still don't see where it says "delete message".

Is it next to some other buttons or something else you see
on your edit screen.

OK....I see the delete screen comes up for every post except
the first post of the thread.

So I assume you have to wait for the thread to expire before
you open a new thread.

Yeah, you can delete any of them except the first one. We used to be able to delete threads, not sure why that feature was removed.

I'd ask a mod to close my old thread if I wanted to start a new one.

personally, whenever i see a thread that should be closed (including one of mine), i say, "die thread! die!".

meh, usually doesnt work though

You take a sawed off shot gun, and shoot it dead center of the first post at point blank range.

Seriously though, I've seen people either edit their first post and ask a mod to close the thread, or add a last post asking a mod to close the thread. I've not actually seen a post get deleted though.