My son and husband are both runners. The best thing you can do is to go to a running store, preferably a privately owned one rather than a chain which just employs clerks who don't necessarily know anything. You need to go to a store that caters to runners - you could ask local running clubs or high school track coaches if they have an arrangement with such a store. Often these pros will give a discount to a school in the hopes of getting a lot of traffic - the chains don't do that. At the store, they should have a treadmill (unless they are in a mall and have a large area where they can watch you walk) - they should watch you walk toward them and away from them, and/or to walk on a treadmill. They are watching for the way you run (such as heel strike - whether you land on your heels or the balls of your feet, and whether you are "even" on both sides) and for pronation (whether you tend to roll inwards or outwards - and again, whether it is the same on both feet). It is essential that you run/walk absolutely naturally when you do this - don't try to adopt a style that you think they want to see. It's about your body's natural rhythm and style -- then they can see what is causing you the problem, and suggest a shoe to compensate. Arch support is important but it is only one aspect. So, spend the money on good shoes, and buy really cheap shorts and shirts! Cut back somewhere else but not on shoes!! Everyone's feet are different - your problem could be a high arch, but then again, you might just have a high arch but that's not causing the problem. Know what I mean? My son has been a competitive runner for 7 years so we've been through a lot of shoes.
Colleges also have deals (sponsorship) with running shoe companies, but by then, the athletes usually know what they need and they just order them directly from the manufacturer, so no one is actually fitting their feet with shoes. However, if you have a college near you and want to ask the coach or trainer for recommendations for a local running store, you can try that. My guess is, you won't have as much luck getting through.
It's okay if you use a store that also sells cross trainers or walking shoes, but their focus should be running. Do not buy on line until you have found a shoe that is absolutely perfect. Then you can replace it. Also, keep track of your mileage - the cushioning can wear out after a while and the shoes need to be replaced. A good running store will be able to check your shoes for you and let you know if there is still life in them. If not, retire the old ones and use them for gardening but not for serious walking or running.
Good luck!