Most of the worlds alcohol is made by growing yeast in an airtight container. So the general recapy is water, sugar and yeast, put in a container with a one way valve that only lets air out for about two weeks. This is all fully organic. The difference in different types of alcohol is mostly how the sugar have been made. All plants have some form of sugar that can be extracted but this often leaves a lot of impurities in the water. This is what gives the different alcoholic beverages their unique taste. It is also possible to destill the alcohol. Yeast is not able to produce very strong drinks as it can not handle too much alcohol. So if you want stronger drinks then wine then you need to extract the alcohol from the water by exploiting the different boiling temperatures of alcohol and water in a destillation aparatus.
It is also possible to make alcohol through inorganic means by using natural gas and putting it through a chemical process. This is sometimes done for certain industrial alcohols where they need to controll the process more tightly. However in most legislation alcohol sold for human consumption have to be organic.
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