You prep that morning by not using any deodorant or powder. This is because deodorant has aluminum chlorhydrate which can show up on x-rays and give a false positive. There's a similar issue with powder, so just don't use either.
You'll probably fill out forms including a sheet asking about any scarring you may have if you've had surgery or the like so they can account for it when they're checking you.
You strip down to the waist and go into a room with a technician (I have never had a male technician). They will position you in several different ways so they can get pictures from all sorts of angles. You'll have to hold positions and hold your breath while they take the x-ray images.
The machine works by pancaking your breasts down. I have been both small and large for mammograms (when I've been thinner or heavier) and I can honestly tell you that it pinches no matter what size you are. That's no reason not to have it done, of course.
If they see something and they want more detail, you might get an ultrasound (which looks just like on TV if you've ever seen a woman on TV getting an ultrasound - same thing except they're checking your breasts and not your uterus).
Either way, they'll generally (at least in the US) get you results in maybe 2 - 3 days on the outside.
Then you come back in 6 or 12 months depending on what they say, and you get to do it all over again.