Learn Finnish: Minä annan jäätelöä.

Jäätelö (ice cream) is a mass noun, meaning it is something you measure rather than count. Because you are giving an indefinite amount (just "some" ice cream, not a whole portion or all the ice cream in the world), the word must be in the partitive case, which gives us jäätelöä.

The English translation says "some ice cream", but which Finnish word means "some"?

There isn't a separate word for "some" in this sentence! In Finnish, using the partitive case (jäätelöä) already expresses the idea of an indefinite amount, so the meaning of "some" is built directly into the grammar of the noun.

How is the partitive ending for jäätelö chosen?

For words ending in a single vowel, the partitive ending is usually either -a or -ä. Because the word jäätelö contains the front vowels ä and ö, the rule of vowel harmony requires us to use the front vowel ending -ä.

The dictionary form for "to give" is antaa. Why does it change to annan here?