I have a friend who is Celiac and can only drink gluten-free beer. How on earth is it made?
These beers are made with non-gluten containing grains such as millet, rice, corn, or buckwheat as opposed to glutenous grains like rye, barley, or wheat.
As a side note, I recommend your friend give Omission Beer a try. I had it once on accident at a social event. I couldn't tell the difference between it and the real thing until I got home and looked it up online.
In general, such beers are made with grains that contain little or no gluten, such as buckwheat, sorghum, rice, or corn.
Incidentally, this also means that cheap macrobrews such as Coors and Budweiser, which are often brewed with the cheapest of cheap adjuncts in their grain bills (such as corn and rice) end up being gluten-free (or very low gluten, legal definitions of the term vary) as well. Because the legal definition of 'gluten free' in many jurisdictions allows for very low quantities of gluten (generally less than 20 ppm), many gluten free beers include small quantities of rye malt for flavoring purposes. While some individual with celiac are able to tolerate these low levels of gluten (as are non-celiacs pursuing a gluten free diet for other reasons), tolerance can vary, so be careful when selecting a gluten free beer, and be aware that they can vary wildly, both in quality, and in gluten content.
Some Gluten Free beers actually have gluten at the moment they are made, for example in the case of Omission the beer goes trough a proprietary "gluten removal process" and then they use a gluten test called the Competitive R5 ELISA, which is used to test foods that are "hydrolyzed," or broken down. This test looks for a specific lengthy fragment of the gluten protein and returns a negative result if it doesn't finds it.
If the test results are under 20 parts per million (as @LessPop_MoreFizz's answer says), then it can be called "gluten free" in the USA... and yes, I've heard people with serious celiac disease can still "feel" that concentrations and get sick.
"Estrella Damm Daura" on the other hand has only 3 parts per million, they also have a proprietary process to remove gluten. Estrella Damm Daura is an European beer made in Spain, obviously in Europe health and food standards are way better than USA's. In Europe, food authorities will never allow a brewery to call a beer with 20 ppm "gluten free". Just don't confuse it with "Estrella Damm" which is their regular beer.
Just to add to this topic, I think it's important that the correct terminology is used since a number of answers contain false information.
In the beer world, "gluten free" can only be used if the ingredients used to brew the beer do not contain gluten. Sorghum appears to be the most popular ingredient for making GF beers, but there are a number of other options including buckwheat, millet, honey, even chestnuts. Redbridge is an example of a GF beer. I have yet to taste a GF beer that I enjoyed as sorghum specifically gives off a cider-y flavor and all the beers end up thin.
There are also beers that are brewed with traditional ingredients that contain gluten, but an enzyme called Brewer's Clarex is added to primary fermentation. Clarex was originally used to clear beer and prevent chill haze, but it was discovered it also breaks down gluten such that, when tested with traditional gluten tests (ELISA), the beer is well within the "gluten free" threshold (<20 ppm). These beers cannot be called "gluten free", though, rather they can only be labeled "crafted to remove gluten". Omission brews "gluten reduced" beer (which are very good IMO), but apparently Yards also uses Clarex in some of their beers (even though they don't label their beer as "crafted to reduce gluten").