The easiest way is to buy a $20 french press. Grind the beans coarsely, so the individual grinds are larger than a grain of sand (you can use a blade grinder, for around $15 on sale, but a more expensive burr grinder will give much better uniformity). Put the ground coffee in the french press. Boil water, but add a couple of tablespoons of cold water before pouring it onto the beans -- the temperature should be around 204 degrees farenheit. Pour the hot water onto the ground beans, stir the resulting slurry, and fit the lid loosely onto the press, without pressing the plunger. Leave for 4-5 minutes. Then depress the plunger, and drink.
The other good low-price option is to get a Chemex coffee brewer, and the square filters that go with it. These run around $30+. Again, very low tech: grind beans, boil your own water, pour it on, and so forth. I'll include a link to more details at the bottom. There are many people who believe this is the best cup of standard-strength coffee you can make.
From there, you enter more expensive territory. Drip brewers are very easy and convenient, but despite their greater cost, the quality is generally not as good as the options above. Typically, water temperature is a little too low, and depending on the design, the water may not properly mix with the slurry. But if you're going this route, try to avoid hotplates, and instead get one that brews directly into a vacuum carafe. Technivorm has a good reputation for raw quality (and looks cool), but comes at a price premium.
I don't know much about the vacpots, but they're also definitely worth a look, and come in lower on the price scale than good quality brewers.
Finally, there's espresso, in which the water is pumped through very finely-ground coffee at high pressure. If you're really looking for a quality product here, your entry point will be at least $200 for a no-frills espresso machine, and another $100 for a grinder capable of grinding for espresso. The cheapest setup I'd recommend is a Gaggia Carezza ($220-ish) and a Solis Maestro grinder (around $100). Don't get a Krups or equivalent espresso machine from a store -- look online, read the myriad reviews, and find something in the right range. If you're willing to go a little higher, the Rancilio Silvia with Rancilio Rocky grinder will allow you to brew espresso that's better than the vast majority of coffee houses, mainly due to the overall low level of barrista training (although you won't have nearly the throughput of a commercial machine).
Hope this helps.