Making good coffee is easy. Get good beans, the definition of “good” depending entirely on your tastes. Grind the beans immediately before brewing, for maximum freshness. Steep the beans in water between 190 and 200 degrees Fahrenheit. Steep the beans for about 4-5 minutes, so as to avoid extracting bitter flavors from them. Done.
Coffee purists will note about a million little quirks of the brewing process that I have omitted, each one they consider essential. More power to them. Perhaps they’re extracting an additional 5% of pure deliciousness from their coffee, but they’re doing five times as much work and spending twenty times as much money in order to get it, so I’ll just pass. I’ve found that the basic steps listed above give me an excellent cup of coffee with very little investment in time and money.
Drip-style coffee makers are the most popular ones in America, by far. The problem with these devices is that they typically do not get the water hot enough to fully extract the good flavors in the oils. The acids in coffee beans are extracted at lower temperatures than the other flavor compounds, which means that cool water produces a sour-tasting cup.
The two simplest and cheapest ways of making a great cup of coffee are the French press and the manual drip method. With the French press, you pour the ground coffee and the hot water into a container, stir it, let it steep, and then separate the grounds from the brew by means of a metal plunger with a mesh screen on it. French press is my favorite way of making several cups of coffee at once. Once the coffee is brewed, you can leave it in the press or, if you have a thermos or thermal carafe, you can pour it into that to keep it hot and fresh. Some people claim that leaving the coffee in the press with the grounds makes it bitter, but that hasn’t been my experience.
One thing I don’t like about the French press is the cleanup. Because I compost, I can’t just swirl the grounds in water and dump them out. That would make the compost too wet. Getting the grounds out is a bit of a pain. And sometimes, I just want a single cup of coffee. They do make single-cup presses, but I don’t have one.
The manual drip coffee method works just like an automatic drip machine, except you manually boil the water and pour it over the grounds. Because you’ve boiled the water before-hand, you know it’s above 190. Technically, you should not brew with water above 200, but I just take the pot off the heat and pour it on. I’ve found that the room-temperature grounds immediately bring the water down below 200, and I don’t taste a difference with water that has cooled to 200 and water that is just off the boil.
If you are a fancy-schmancy-pants, you can buy a Chemex Drip Coffee Carafe for$40. Despite what they say about their high-falutin’ filters, Chemex is just a fancy glass container with a coffee-filter-holder on top.

May I point out that glass containers are actually not so great for storing coffee, because they don’t hold the heat well. A thermos or thermal carafe is a better choice for storing coffee you don’t intend to drink immediately.
If the price of the Chemex puts you off, you can spend about $12 to get a manual drip pot like the one below.

But I’m a cheapskate. If, like me, you have perfectly good funnels sitting around your kitchen, you might consider my method, documented here for all posterity.

And if there is anything to those high-falutin’ Chemex coffee filters, I bet they still work just as good in a $2 plastic funnel as a $40 glass pot. I think that Alton Brown would be proud.

 
#1 by Lee at December 8th, 2009
Why have I never thought of this. Freaking genius.
#2 by M at December 20th, 2009
Those glass things are silly, I’ve used one. Coffee goes right cold. Doesn’t taste any better than a French press (my method of choice).
You can also just make a teabag thingie with the filter, or rubberband it around the rim of the cup, to stay on, as you pour hot water.
Me, in that situation, I’d just go with Turkish/cowboy coffee.