Learn Dutch: Het huiswerk is bijna af. - The homework is almost finished.

Both af and klaar can mean "finished" or "done". However, af is usually used for tasks, projects, or things you are making (like homework or a painting) to say they are fully completed. Klaar is a bit broader and can also mean "ready" to do something (like being ready to leave).

I thought af meant "off". Is af zijn a special phrase?

Yes, af often translates to "off" or "down". But the combination af zijn (to be finished) is a very common fixed expression in Dutch. When you finish building, writing, or creating something, you simply say it is af.

How do I know if huiswerk is a de or het word?

Huiswerk is a compound word made of huis (house) and werk (work). In Dutch, compound words always take the article of their very last part. Because it is het werk, it automatically becomes het huiswerk.

Can I say this sentence in the plural if I have a lot of homework assignments?

No, just like in English, huiswerk is an uncountable noun. You always use it in the singular form, so it is always het huiswerk is, no matter how much of it you have to do!