Make it Strong!
Roasted coffee is perishable and should be kept cool & dry in an air-tight and light-tight container. Stored well, whole bean coffee is great for a couple of weeks and good for a bit beyond that. Ground coffee loses flavor very quickly.
Making good coffee requires:
Good Water: bottled, purified or filtered water - you'll definitely notice a difference. Distilled water doesn't cut it.
Good Coffee: Freshly roasted, whole bean coffee, ground just before brewing. Use 2 level+ tablespoons (bigger than teaspoons) for 6 oz. water as a rule, but experiment until you get what you like. (10-12 cup auto-drip machines are based on 6 oz. cups).
Proper Temperature: The water hitting the coffee should be between 195 and 205 degrees
Correct Grind: Coffee should be ground for the brewing method you use, not some factory generic setting. Use a burr grinder before a whirly blade grinder, but use the blade grinder before buying ground.
Good Brewing Device: So many choices, but water temperature and time are key here - you want the water between 195F-205F (not yet boiling) and it should be in contact with the grounds between 3 and 7 minutes for optimal extraction.
French Press is a great choice. Grind medium to coarse and expect a few fine grounds in your cup
Auto Drip is the most common method. It should use a cone filter and paper filters trap more grinds (and oil) than metal ones. Grind medium-fine to fine. Use room to body temperature water (not cold) since many machines sent the hot water to the brewhead via a tube that runs through the reservoir, which can cool it down too much.
Filter Drip is a great portable choice if you have a hot water source. Paper cone is preferred with a medium-fine to fine grind.
Aeropress is a newcomer with lots of buzz. Ignore the hype and use it to make a good cup or two of coffee concentrate (add hot water to taste) at a time. Requires Aeropress filters and a medium fine grind.
Espresso Makers range from manual to super-automatic, but they all require a fine/espresso grind.
Vacuum Pots are fun and make a great pot of coffee. Try the same ground as the drip makers, or back off to a medium coarse grind if that's too strong.
Moka Pot is a stovetop "espresso" maker. Careful with the standard aluminum ones, and look for a stainless model with a pressure relief valve if you're in the market for one. Use a medium-fine to fine grind, like the drip methods.
Only brew what you can reasonably drink in 20 minutes or so. Thermal devices will buy you some time, but "hot after 4 hours" doesn't mean good after 4 hours.
Don't reheat coffee! (unless it's a real, dire, complete emergency)
Don't re-use grounds! (Well, not for coffee anyway -- they do make good compost.)
You need to keep your brewer clean! Try the Urnex line of cleaners or use a vinegar solution. (Follow this link for details and alternate techniques)