Is it made brewed in such a way as to have no alcohol, or is it just normal beer with the alcohol removed, or some other process?
Non-alcoholic beers (in the U.S., no more than 0.05% ABV) begin their lives like every other beer; they go through the same 8 step process outlined here, but one step is added between the last two steps -- the conversion.
The beer has already been fermented when added to a conditioning tank, where it is left to mature for several days (the 7th step), from here it is cooked to remove the alcohol. Due to the absurdly high boiling point of water (100°C), it is easy to evaporate the alcohol (boiling point = 78.3°C) and leave the rest of the beer behind. Vacuum evaporation is also used in most modern breweries to preserve flavor and speed up the process.
Another method used is reverse osmosis, which allows the water and alcohol to escape from the beer through a membrane. The alcohol is then distilled from the solution, and the water is added back to the sugary syrup originally left behind, reforming the beer (minus alcohol).
The beer is now non-alcoholic and continues to the last step of the brewing process where it is filtered, carbonated, and stored (until it is packaged for sale).