Has this ever happened to you? You go to the shoe store, get your feet fitted for shoes, and they fit perfectly. Then by the time you finish your first run, they are so tight that you have trouble getting them off. This is a not uncommon problem, and it comes from trying on shoes in unnatural conditions.
When you purchase your running shoes, the easiest thing that you can do to ensure the best fit is to never visit the shoe store first thing in the morning. Wait until mid-afternoon or early evening, when you have been on your feet all day and your feet have had a chance to swell to their normal size. In fact, if you can go to the shoe store shortly after a run, your feet should be right around the size that they will be when you finish a run in the new shoes that you are about to buy!
Also, be sure to bring any socks or insoles that you plan on wearing with the shoes. That way, you can make sure that the whole combination works out to get you shoes that are the best possible fit while you are out running.