You use the indefinite article "a" when you are talking about one of something, but not a "specific" one: you use the definite article "the" when talking about a specific one.
To make a general statement about a countable noun, you therefore use either the plural or the indefinite article "a".
Cockroaches are disgusting
A cockroach is disgusting
The plural is the best choice in most circumstances: you might use the indefinite article if, while making a general statement, you are thinking about just one of the subject:
A car can be very expensive to run (I only want one car)
A cat is a better pet than a dog (I only want one pet)
It is possible to use the, but only if you sneak an indefinite article later. This usage is uncommon:
The cockroach is a disgusting creature
For uncountables, no plural is possible and you do not use an article either
poverty is disgusting
The object follows the normal rules, depending on how many of the object one individual subject likes/loves/needs. Remember that hockey is uncountable...
A man needs a maid -- Neil Young song title
Men need a hobby
Horses like apples
Americans love playing hockey