IN the pool when you are talking about being inside the actual pool filled with water. AT the pool when you are referring to a public swimming facilities that contain a pool. So if you have a pool at home, you swim IN the pool every morning. But if you take swimming lessons at a local swimming centre, you swim AT the pool every week. Of course, once you arrive at the pool, you will swim IN the pool that's AT the pool ;-) And I shop 'AT' or 'IN' the supermarket? Both a pretty much interchangeable for me. I saw him in/at the supermarket. I work in/at the supermarket. They sell this pasta at/in the supermarket. I think AT sounds more natural for me for all of these cases, but IN would not sound too bad to me personally.

You use "in" when a region, usually with clear limits, exists. When you use "in the supermarket", the so-called limits are the walls of the building. "In the pool" suggests the sides of the pool, or at least the area of water. You use "at" when you talk about a point in a longer journey. You [go to] a place, then you [are at] a place. If you travel from your office, to the pool, to the supermarket, and then to your house, then you use "at" when talking about the moments you were there.