It may seem obvious, but there is more than one way to change a hubcap. This is due to manufacturers taking a different approach to the problem of protecting their wheels. Originally, hubcaps were meant as a protective cover for the hub. This is where the spokes attach to the circle in the center of the wheel. The hubcap kept out the water and dirt, keeping the hub in good shape. Over the years some versions expanded to include the entire wheel, becoming known as wheel covers. Whatever you call them, here is how to remove and replace a hubcap.
First, assess what you have. A modern hubcap covers just the hub, usually covering the lug nut bolts, or just inside them. They can be plastic or metal, and held on by internal clips or external screws. If it is held on by clips, it can usually be removed with just a screwdriver. Look to see if there is a slot where a prying device is meant to go, as some manufacturers built that specific section for prying. If not, carefully work the screwdriver under the hubcap at the edge, and pry outward. It should pop right off. Now for screws, you have to consider what type is needed. Some require standard Philips head screwdrivers, while others require Torx bits. Either way, undoing the screws should result in the hubcap popping off. Remember that some vehicles, like certain years of the classic Volkswagen Beetle, need a specific tool for this job, and a screwdriver simply will not do.
Now for wheel covers, the process is a little different. Check to make sure they are not secured to the wheel by fake plastic lug nuts. This is common among modern sedans with their original equipment wheel covers. They are usually on tight, so a lug wrench is recommended. Once unscrewed, the wheel cover just pops right off. For the wheel cover without screws, remember that it is held on by pressure from a metal band and plastic clips. You do not want to break the metal clips that hold the band, or bend the band itself, so work carefully. Find an area where the outer rim is thicker, like where the spoke meets the rim. Work the screwdriver under the rim and carefully pry outwards. You will most likely have to approach from a second, or even third angle, as too much pressure on one area can snap a plastic wheel cover. Once you have it loose at a couple of points, it should pull right off.
Re-installation is simply the reverse of the above instructions. Finally, wheel cover and hubcap removal tools are sold in auto parts stores and online, and are really affordable. They are much less likely to damage or break your hubcaps. If this is a common maintenance item for you, consider getting a dedicated tool to make your life easier.
To see the process in action, check out this video: