deze, die, dit, dat: this and that in Dutch

A demonstrative is a pointing word — English this, that, these, those. Dutch has four: deze and dit (this/these, for something near) and die and dat (that/those, for something further away). Which one you pick depends on the noun: deze man (this man) but dit huis (this house).

Two things decide it at the same time: whether the noun is a de-word or a het-word, and whether you mean something near (this/these) or far (that/those). de-words and all plurals take deze (near) or die (far); het-words take dit (near) or dat (far).

1. Check the noun's gender — see de or het?. A de-word takes deze or die; a het-word takes dit or dat.
2. Check the distance: something near you takes deze or dit; something further away takes die or dat.
3. Remember that every plural is a de-word, so plurals only ever use deze or die, whatever the singular was: het boek → deze boeken / die boeken.

A memory hook: de, deze and die all carry the -e of de, while het, dit and dat all end in -t like het.

• Right before a noun, in place of de or het: Deze trein gaat naar Amsterdam. (This train goes to Amsterdam.) Dat boek is van mij. (That book is mine.)
• On its own, once it is clear what you point at, with the noun left out: Welke wil je? Deze. (Which one do you want? This one.) More on this in die and dat as replacements.
• To introduce or present someone or something, Dutch uses dit (near) or dat (far) whatever the gender or number: Dit is mijn zus. (This is my sister.) Dat zijn mijn ouders. (Those are my parents.) The pointing word stays singular dit/dat even next to the plural verb zijn.

When introducing people or things, English speakers reach for a plural word by analogy with these/those and say Deze zijn mijn ouders. Dutch keeps the singular dit or dat here: Dit zijn mijn ouders (These are my parents), Dat zijn leuke schoenen (Those are nice shoes). Do not let the plural verb zijn pull you toward deze/die — in this introducing pattern the pointing word does not change for number.