Whether you're stuck in the store choosing between a slightly snug 9.5 and a too-big 10, or you're wearing your brand new shoes out for the first time and want to make sure they're comfortable, a hair dryer and some thick socks are all you need to make sure your new pair are ready for a night on the town. This is a variation on a very old trick from back in the day, but it still works like a charm. Just put on a pair of thick socks over the socks you want to wear with the shoes (thick winter socks), and shove your feet into those shoes. They should be tight, that's OK. Then get a hair dryer, and -- assuming your shoes are a natural material, not plastic or anything that will melt -- run the dryer over the tight parts of your shoe until they feel a bit better. Maybe it's over the bridge of your foot, or the toebox is a little tight. Either way, run the dryer until you have the flexibility you want. Turn the dryer off, walk around in the shoes a bit and wear them until they completely cool, and you should be good to go. Take the heavy socks off, and see how well they feel, and repeat as necessary.
Aaron Marino of IAmAlphaM goes through the whole process in the video above (skip to 3:00 for the actual demo, but the setup is good). He also explains there's more to a pair of shoes that are slightly snug than "well you should have gotten the right size". Maybe you're in between sizes, or, as we've learned, your feet swell over the course of the day, so a pair you want to wear tonight may have felt better when you bought them earlier a few days ago. Either way, all isn't lost, and with a little work you'll be comfortable in your new shoes.