Three main choices, I suppose:
1) drip (the water is poured, or delivered, over the coffee grounds in a paper or metal filter - this is the method we use at home);
2) percolator (delivers a 'thicker', richer coffee - a friend of mine is still using the percolator his parents acquired in the 1960s, it makes a great cup of coffee);
3) French press (which my friend in Somerset uses - tasty).
The drip filter method is the quickest to prepare and easiest to clean up, I think. But probably does not deliver the best tasting coffee.