The two main fit issues to consider when choosing a running shoe are gait pattern and size.
Gait: Your gait is how your foot rolls from initial ground contact to toe-off. Most people strike on the back lateral portion of their heels and then end up pushing off near their big toes. Rolling inward too early or severely is called "overpronation. " Overpronation can throw your alignment out of whack and lead to injury. Rolling outward is called "supination" and can also lead to injury. Brooks offers several types of running shoes for different gait cycles. These range from Neutral (for the biomechanically efficient) to Control (for those who need the most aggressive pronation control).
Size: We generally recommend that you order your Brooks running shoes 1/2 size to one size larger than normal dress shoes. For men's footwear, "D" is the default width when no width is otherwise specified. For women's footwear, "B" is the default width. You can tell that you have the right size when there's about a thumb's width distance between the tip of your big toe and the top of the shoe. This allows extra room for any swelling that might occur on longer runs. Also, make sure that your foot is not spilling over the footbed on either side. If it is, consider a wider width.
Please note that the H at the end of a shoe size does mean it is a ½ size.