Learn Polish: Musisz mieć sto punktów. - You must have a hundred points.

This is the main rule for numbers 5 and above! When you use a number from 5 onwards (like sto), the noun that follows it must be in the genitive plural case. So, the regular plural punkty (points) becomes the genitive plural punktów.

How do I know to add -ów to make the genitive plural of punkt?

Punkt is a masculine noun that ends in a hard consonant (the letter t). For most masculine nouns ending in a hard consonant, the genitive plural is formed by simply adding the ending -ów.

Does the word sto change its form because it is the object of the verb mieć?

Not in this sentence. The verb mieć (to have) requires the accusative case for its direct object. For the number 100, the accusative form is exactly the same as its basic dictionary form: sto.

Why isn't there a word for 'a' or 'one' before sto?

In Polish, the word sto by itself means 'a hundred' or 'one hundred'. You do not need to add jeden (one) before it unless you are strongly emphasizing the exact number.