"Amaris has to tell Baz stuff but the scene is wooden"

This question popped up recently on a forum: "I've just reached a point in my WIP where two characters get together after a while apart and one has to tell the other what's been happening. It's important stuff. I haven't found it easy, but I never find it easy to write the 'telly' stuff - particularly the links between the telling and the rest of the scene that is happening around them. Anybody have any words of wisdom?" There were some good responses, and I found mine developing into a blog post, so here we are. The first thing is...