You want to give yourself plenty of time to try on a variety of styles, models and sizes. The best time to shop for shoes is at the end of the day or after a run. That's when your feet have swelled to their maximum size. Even if you know your size, have both feet measured. If the sizes differ, fit the larger foot.
Sizes vary among brands.
Judge a shoe by how it fits your foot, not by its listed size or by what you think your shoe size is. Wear the socks you expect to run in. If you wear orthotics, put them in the shoes you're considering. Stand during the fitting process. When you run in a swimming pool, the water's resistance creates a full-body workout, while the buoyancy eliminates the impact on your legs.