Beer is an alcoholic beverage that results from process called brewing that uses malted grains, hops, yeast, and water. During brewing saccharification of starch and fermentation of the resulting sugar that produces the alcohol. The starch and saccharification enzymes come from malted cereal grains such as barley and malted wheat. Corn and rice are used as well. Hops are used for flavoring and as a preservative. Variations may result from using other ingredients such as fruit, herbs, and spices
Ales are brewed with "top-fermenting" yeasts at close to room temperatures, 50-70F (10-21C). Ales encompass the broadest range of beer styles including bitters, pale ales, porters, stouts, barley wines, trappist, lambic, and alt. The British Isles are famous for their ales and it is a popular style with homebrewers and micro-breweries.
Lagers are brewed with "bottom-fermenting" yeasts at much colder temperatures, 35-50F (2-10C) over long periods of time (months). This is called "lagering". Lagers include bocks, doppelbocks, Munich- and Vienna-style, Maerzen/Oktoberfest, and the famous pilsners. Pilsner beer originated in the town of Pilsen, now in the Czech Republic and was the first non-cloudy beer. Most popular beers produced by the large North American breweries were originally of the pilsner style. These have diverged a great deal from the original style and succeed now by the force of the mass-marketing prowess of the brewers rather than any remarkable qualities of the beers themselves.
"Dry" beer was developed in Japan. Using more adjuncts (like corn and rice) and genetically altered yeasts, these beers ferment more completely and have less residual sweetness, and hence less aftertaste.
The making of "ice" beers, in general, involves lowering the temperature of the finished product until the water in it begins to freeze and then filtering out the ice crystals that form. Since water will freeze before alcohol, the result is higher alcohol content. The ice forms around yeast cells, protein particles, etc. so these get removed as well; leaving fewer components to provide taste and character.
Technically speaking, draught beer is beer served from the cask in which it has been conditioned. It has been applied, loosely, to any beer served from a large container. More recently, it has been used as a promotional term for canned or bottled beer to try to convince us that the beer inside tastes like it came from a cask. See also "Real Ale".