I don't think pedestrians have the right of way here. In fact, I know they don't. In order to cross the street, first you must decide which way to look first (you look right - it took me a week to figure that out) and then you have to be totally sure that no one is coming. If a car is coming, they will not stop. I've heard engines gunning for me. I have heard rumors that if a pedestrian is hit, the pedestrian has to pay for damage to the car. I'm not sure that is true, but I'm still careful.
I definitely don't mean to say that I never walk in St. Andrews. I have to. I haven't figured out the bus system, and most of my classes are in St. Mary's College on South Street, which is a good 15 to 20 minute walk from my dorm room in New Hall (Side note - New Hall is a Three-Star rated hotel used in the summer by golfers). St. Andrews itself is a small town, with four main streets:

Map of St. Andrew's with some cross streets and alleys.
I've managed the crosswalks so far. Crosswalks here look a little like those at home, although they're accompanied by flashing lightpoles, which I don't yet understand. There are also two of the kind that have the button and the red light, and they work fairly quickly and beep loudly when you're allowed to cross.
There's also plenty of space for leisure walking, if you want to avoid the cars. St. Andrews lies on the Fife Coastal Path which runs right in front of the Old Course Hotel and up along the cliffs of the Scores and right by all of the ruins. Here's a picture of me on the East Sands side of the path, and an example of the view from the path:

On the other side you can see the ocean. So, I guess getting around here isn't all that bad, as long as you know what you're doing.