Okay, I admit I do this more often than I would like. It happens everywhere, but especially in the UK, where the accents can be formidable for me to understand. Here goes:
1. At first, ask for repetition. Lots of it. When person looks startled or puzzled (since most hearing people aren't used to repeating/ making themselves clear), apologize and explain that you are deaf. Point to space-age-looking CI for "proof."
2. Explain to person that you need him/her to slow down, etc. Chances are he/she won't do this longer than about two seconds, but try anyway.
3. Focus as hard as possible, mentally scolding CI for flitting off to ooooh and ahhhh at noises several yards away.
4. Apologize some more when the conversation starts to seem non sequitur.
5. Realize, with a sinking feeling, that person is going to be impossible to lipread. Wonder if you should tell him/her this, then decide that this bluntness would be rude. Start thinking of alternative strategies to salvage the situation until you can extricate yourself.
5. Alternative strategy number one: watch person's face and nod encouragingly at strategic moments. This is known as the "deaf nod." (Oh, how you hate it.) Add "yeah," and "okay," and "right," when deemed appropriate.
6. Alternative strategy number two: keep the focus off of yourself. Ask questions. Try to figure out what person is talking about, if possible, and ask who/what/where/why/how/anything at all. As long as person is talking, he/she will be appeased. Even if you are not.
7. Alternative strategy number three: change the subject constantly. Make arbitrary comments and ask person what he/she thinks about them. Control the ball, try to ease the conversation into a place where you can feel comfortable.
8. Inevitably think about how ridiculous this is getting. But you've gotten through worse, so take a deep breath and keep going.
9. Alternative strategy number four: parrot person's words back to him/her, watch for validation that this is indeed what he/she said. If you're right, run with it. If you're not, back to square one.
10. Alternative strategy number five: if other acquaintances/friends come along, gratefully pass the conversation off to them. Let the group ramble along, insert a comment or two whenever possible, but otherwise sit and silently reassure yourself that you're okay, that silly situations like this don't reflect on your self-worth.
11. Alternative strategy num - heck, forget these strategies! This isn't working, and you're tired of pretending and wasting your time. Come up with an excuse to leave. Walk away feeling somewhat abashed, even though none of this was your fault.
So, most of the time the CI still hasn't quite kicked in for speech comprehension, especially with an unfamiliar speaker. The most frequent problem is simply that I can't pick out a person's voice from amidst other distracting noises: objects being moved around, other people chatting, cars passing, etc. Overstimulation leaves me unable to focus. When background noise isn't an issue, the CI does help guide and ease the pressure from lipreading, but it still can't stand alone in terms of understanding everything. That auditory memory of mine is developing, yes, but slowly. I'm realizing how much of a baby brain I've got to work with. That brain tries very hard, but it needs time. This is certainly an exercise in being patient!