"He has our dog."
Translation:Hij heeft onze hond.
There was some info on it in the very first Basics 1 lesson group. Basically, het is used with neutered singular nouns (i.e. singular nouns that don't have a gender), while de is used with gendered singular nouns and all plurals.
Figuring out which nouns are gendered can be tricky, though. Dutch isn't like the Romance languages where the last letter of the word pretty much tells you its gender. In Dutch, the words that refer to males or females are obviously gendered, but after that it's kind of just experience (at least from what I've noticed).