Common uncountable nouns refer to things that cannot be counted individually, such as 'advice', 'air', and 'water'. These nouns cannot typically use the indefinite article 'a' or 'an' and are made countable using constructions like "a glass of water". The document provides a list of over 80 uncountable nouns in English along with some examples of how they are quantified, such as "a bottle of water", "a piece of equipment", and "a slice of cheese".