Singular means one. Plural means more than one. Non-count nouns can, by definition, not be counted. Therefore, they can be neither singular nor plural. Only count nouns can be singular or plural.
For example, consider the count noun course. It can be singular as in:
My roommate has taken a physics course.
Or it can be plural as in:
My roommate has taken several physics courses.
In most cases, in order to change a singular count noun into a plural count noun, English adds an the ending -s. Some nouns, however, add -es, including nouns that end in -ch (church/churches), -sh (dish/dishes), -ss (princess/princesses), and -x (fax/faxes). Other nouns that end in a consonant followed by -y, change to -ies in the plural (poppy/poppies).
However, there are many exceptions that must be learned individually with the help of a dictionary. For example, some nouns don't change spelling in the plural (sheep/sheep) or change in dissimilar ways (man/men).
The two factors discussed above, count versus non-count and singular versus plural, have a big impact on the English article system. Before we take a closer look at that impact, however, we have to consider two additional factors.