My dog's a PAT dog - you'll be contacted by the area coordinator who'll arrange a time for you and your dog to be assessed. It's usually somewhere like a garden centre cafe, somewhere where there'll be people (and food) but not crazily busy.
The assessment is pretty straightforward - we had to demonstrate loose lead walking; my dog had to take a treat gently from the assessor (he does this ludicrously carefully, it's very funny to watch as he sort of purses his lips to make sure his teeth are nowhere near your hand); the assessor will want to see how your dog reacts to sudden noises like a metal tray falling to the ground - being startled is fine, being terrified probably not - and they'll want to see that your dog doesn't jump up, paw, whine or bark for attention. At one point in our assessment a little boy toddled over to my dog and whacked him on the side (he was trying to stroke him rather clumsily) and my dog just turned to look at him, saw it was a very small child and wagged his tail gently - it wasn't part of the test but his reaction gave him extra brownie points!
It takes a little while to get the application processed as the charity is run by volunteers so don't worry if you don't hear immediately.
My dog spent some time being a reading dog at one of the local primary schools which he really enjoyed but we stopped after about 18 months as my work changed and my dad needed a lot more support on my days off. My dad's now in a nursing home so I take my dog with me when I go to visit and we also visit some of the other residents.
My dog definitely knows when he's 'working' - once the coat goes on, he's got his 'sensible' head on