First you have to try them on before buying. Do this towards the end of the day as your feet are slightly larger than early on in the day. Feet come in many different shapes as well as sizes. Different brands tend to cater to different foot shapes so you need to find the brand that tends to work for you. For me that's Merrell. Other brands like Vasque, Solomon, etc are always too tight on my feet regardless of size.
The toe box volume, i.e. height and width is most important. You need to be able to easily wiggle your toes as feet swell during a long hike. Find a boot that allows for ample toe box room and with lacing that allows the toe box to stay generous and then locks your foot in that position, so that when going downhill your foot will not slide forward in the boot.
Heel cup size matters as well. With the boot comfortably laced, your heel should not lift at all while walking.
Once you find a boot that fulfills ALL these requirements, that is your boot, your fit, your size. There is no need to go a size or half size up. But if you find the right boot but can't decide say between the 9 or 9 1/2, always pick the larger one.
Also as you age your feet get larger, particularly in spread. You don't notice this much until into your 40's. If you are 50 or older this 'spreading' can progress rather rapidly so a boot that fits properly may become tight over the space of just 1-2 years.
With all this in mind, i suggest you visit a number of different stores that carry good hiking boots and try on as many different brands as they carry. When you find the brand that fits your foot shape, you will know it. If you have to try to convince yourself even slightly, it is not the right boot. It must be perfectly comfortable in the store such that you don't feel like taking them off. Don't let the salesman tell you "Oh, they will stretch a little or mold to your feet". If they are not perfectly comfortable in the store, they never will be.
Finally, type of hiking is important. Steep hikes with a heavy backpack in mountainous terrain require boots with a stiffer sole. For less aggressive terrain, a sole with flex makes for more comfortable walking.
Also not every boot with the same specs in the same brand fit exactly the same. i.e. if you find a Merrell 9 1/2 EE that really seems perfect, buy that pair. Going back later and getting a different pair of the same boot in the same size can give you a boot with slightly less of a perfect fit. Hence: "if the shoe(boot) fits, wear(buy) it".
Roland