I eat a package of Oreos beforehand to help out, that way the hygienist has a clear marker of if they've cleaned somewhere or not. Cleaning clean teeth would be like painting a grass green. Did I get that spot? But painting it purple, you know where you've been.
My dental hygienist is cute. Every time I visit, I eat a whole package of Oreo cookies while waiting in the lobby. Sometimes she has to cancel the rest of the afternoon's appointments.
Do you wash your hair before getting a haircut? Out of respect for the professional, always clean yourself before they have to get up close and personal.
I brush my teeth beforehand. There were a couple of times when I didn't, which led to the dental hygienist picking at my teeth and gums a lot more than when I did brush. I'd rather brush and get rid of as much crud from my teeth that way as opposed to having spend more time and pain at the dentist.
Do you want to be done with the picking and scraping as easily and quickly as possible? Brush first. Not excessively, just as you normally would at night. If you're flossing, do it a couple hours early so any swelling can subside before they measure your gums.
Otherwise it's like trying to mop an unswept floor.
Dental assistant once thanked me profusely for brushing my teeth before the appointment. I always do, but that cemented my resolve to continue doing it indefinitely.
I brush my teeth like normal usually unless I eat something like ribs, then I might brush/floss right beforehand. I'm in the habit of brushing twice a day and flossing regularly already though, so my teeth are usually relatively clean anyways.
I would never brush or floss before, unless I had just eaten something awful within the last hour or so. I think it is best to stick with your normal routine. You give the hygienist a better look at how good or bad your cleaning is. They can easily tell what is recent and what has stuck to the teeth and requires scaling. Furthermore, you aren't saving them any stink. The stuff that you need their help to clean out smells about 50 times worse than the things you just ate (just smell your floss compared to your breath after any meal). A quick rinse with water will get the worst out of their way, and even if you're a sloppy eater the rest will take maybe 5 minutes at worst to remove.
My orthodontist had a teeth brushing station with disposable toothbrushes (that come pre-loaded with toothpaste). I've never seen that at a dentist though. Mine have always given out toothbrushes at the end of an appointment. Probably because otherwise people would keep using the same one for years.