Learn Polish: Chłopiec otworzy drzwi. - The boy will open the door.

The verb otworzyć (to open) is a perfective verb, meaning it describes an action that gets fully completed. When you attach a regular present-tense ending like the -y for he/she/it to a perfective verb stem, it automatically creates the future tense. This is because a fully completed action cannot happen right now in the present moment.

The English translation says 'door', but isn't drzwi a plural word?

Yes, it is! In Polish, drzwi is a plural-only noun, much like the words 'glasses' or 'pants' in English. Even if the boy is opening one single door, you still must use the plural word drzwi.

What grammatical case is drzwi using in this sentence?

It is in the accusative case because it is the direct object (the thing the boy is opening). Luckily, for inanimate plural nouns like drzwi, the accusative form is spelled exactly the same as the basic dictionary form.

How would the verb change if I wanted to say 'I will open'?

You would swap the he/she/it ending (-y) for the 'I' ending. For this specific verb group, the first-person singular ending is -ę, which makes the word otworzę.