Coffee can be made many different ways, and the method you choose can have an effect on the taste of your final cup.
This is likely the method you are most familiar with, as nearly every home in the country has a basic coffee maker like this. Coffee grounds are placed in a filter basket inside the machine, and the internal reservoir is filled with water. The machine heats the water and the hot water drips through the grounds into a glass carafe to produce brewed coffee. It's fairly simple, quick and the machines are inexpensive. It's the preferred method for most people because the entire process is automatic and requires no skill on your part.
2. French Press
The french press, is also known as a plunger pot, and is another very popular way to make coffee. Your coffee grounds are added directly to a pot of hot water, and after they "steep", you press down a plunger inside the pot to strain the grounds to the bottom of the pot. It's another pretty simple way to make coffee, and is a preferred method for those who don't really make enough coffee to warrant another piece of kitchen equipment.
Though the percolator has fallen out of favour over the years, it's still used (mainly by older coffee drinkers who have always used one). Admittedly, the coffee is not going to be of the highest quality when brewed with a percolator, but I felt it should still be included since people do use them. A basket of grounds is placed in a kettle, and the water is boiled. The boiling water bubbles up through the grounds, where you can see it in a glass bubble at the top of the percolator. When it gets to the right darkness to your taste, it's ready.
Now we're getting into some of the more exotic methods of brewing coffee. These are quite beautiful to look at, but you aren't likely going to find one in your average kitchen. The device has 2 jars, connected on an elaborate, balanced stand. Coffee grounds go in one jar, and water in the other. The water is heated and it flows over to the jar with the grounds. As the water continues to boil, the water jar eventually empties and the stand then tips to the side and the brewed coffee flows back to the water jar. Follow the link for a more detailed description of how this brewer works. Sounds odd, but it's really quite elegant.
Like the balancing siphon mentioned above, you're not that likely going to find an ibrik in your average North American kitchen. An ibrik is a small metal cup on the end of a fairly long handle, and is a Turkish tool for making coffee. The pot is narrower at the top than at the bottom, which is an important feature. The cup is filled with water, and a spoon of finely ground coffee is added on top. The powdered coffee "caps" the water, and as the boiling water bubbles it steeps through the grounds. After the water foams up 3 times, then you know the coffee is done.