There are surprisingly many different kinds of bottle openers out there, but the two most popular by far are corkscrews and bar blades or crown cork removers. Corkscrews are used for opening bottles with corks, such as bottles of wine or champagne. To use them, you just screw them into the cork, and then push down on the sides and pull the cork out.
Bar blades and crown cork removers, on the other hand, cannot open corked bottles. They are basically just the end section from a corkscrew, used to quickly open capped bottles. There is nothing they can do that a corkscrew can’t, but they are much smaller, easier to carry and cheaper to manufacture. These kinds of bottle opener are often stuck to tables or walls, making it easy to just grab a bottle and open it. You can even get them on belts!
For all bottle openers usually being so cheap and disposable, it’s still surprisingly easy to find yourself without one. In this situation, the best thing to do is to simply use a knife (make sure to use the side that isn’t sharp) or some other pointy object, such as a screwdriver. In the original 1891 bottle cap patent, this is actually how the inventor of the crown cap that is now used everywhere, William Painter, says that his caps should be removed – he didn’t invent the bottle opener until two years later. Note that it is a very bad idea to try to get a bottle cap off with your teeth, unless you weren’t fond of them anyway.