In the old times, going to a proper running shop and getting advice. Once you know if your form (e.g. front foot, heel strike), whether you have pronation and then foot size/shape (measured rather than the size shoe you've always had), it knocks about 75% of the range out. In a shop, you can knock that in half because half will be an instant 'no' as soon as you've done the laces up. Some shops will have a treadmill to try the shoes (or for gait analysis), some let you run them outside the shop a bit. I've bought from shops where you can bring them back having worn them for quite a long time. Personally I find that if I find them ok for a few hundred metres then even if they start to become uncomfortable at distance, they will wear in. I'd never buy a pair of shoes and expect to be able to run more than 5-8km on the first 10 outings.
At the moment, I've bought the exact same shoe as I previously had. Some models come in 'standard' and 'wide' fit - unfortunately some online retailers don't specify which one they have, so you can end up with the narrower version of the shoe that would fit in the wide fit.
Most brands that have width fittings will specify. Innov8 have fittings 1-5 (5 is widest) and state on their website which fit each model is. Some brands are known for being wide or narrow - for example, generally Salomon are a narrow fit, Altras are a wider fit. I know there's no point in looking at the Salomon range. I also need a zero drop shoe as I'm a front-foot runner (my footprints don't have heels at all). Knowing this massively narrows down what I'm looking at online. I also know a lot of other runners, so can get recommendations for what is a good shoe for people like me based on terrain. After that, it's a bit trial & error. My biggest problem is finding off-road shoes that a good fit and have good grip on multi-terrain. The terrain here is fairly extreme, simultaneously muddy and rocky, but with road sections between.
I find that I can get away with a wider range of off-road shoes than on-road shoes. I can break in most off-road shoes provided they generally fit - there's a lot more give. Road shoes, not so much. If they aren't right, I'll be heading toward injury.