der Mann, der hier arbeitet

This is the step that makes your German sound grown-up. Instead of two short sentences — Das ist ein Mann. Er arbeitet hier. — you say one: Das ist der Mann, der hier arbeitet.

Structurally there is nothing new. A relative clause behaves exactly like a weil or dass clause: comma, then the clause, and the conjugated verb goes to the end. You have been doing that since Lesson 3.

comma · relative pronoun · … · conjugated verb (end).

The relative pronouns are words you already know — they are the definite articles.

Only one form differs from the article you already use: masculine accusative den. Everything else is der / die / das / die, unchanged.

• Das ist der Mann, der hier arbeitet.

  That is the man who works here.

  der Mann → der; he is the subject of arbeitet

• Das ist die Frau, die Deutsch spricht.

  That is the woman who speaks German.

• Das ist das Auto, das ich kaufen möchte.

  That is the car that I want to buy.

• Das sind die Freunde, die in Berlin wohnen.

  Those are the friends who live in Berlin.

Now the part worth slowing down for, because it is the only genuinely new idea in the lesson. Two different things decide the pronoun, and they come from two different places.

Gender and number come from the noun outside. Case comes from the job the pronoun does inside its own clause.

So der Mann fixes "masculine singular" — that never changes. What can change is whether the man is the one doing something (nominative der) or the one something is done to (accusative den).

• Das ist der Mann, der mich kennt.

  That is the man who knows me.

  he knows → subject → der

• Das ist der Mann, den ich kenne.

  That is the man whom I know.

  I know him → object → den

• Das ist die Frau, die ich gestern gesehen habe.

  That is the woman whom I saw yesterday.

  feminine accusative is still die — nothing to change

• Das ist das Buch, das ich gelesen habe.

  That is the book that I read.

A quick test you can run in your head: replace the pronoun with er / ihn. …, er kennt mich → der. …, ich kenne ihn → den*. If ihn fits, the pronoun is den*.

In English you can drop the relative pronoun — the man I know. In German you never can. Der Mann, den ich kenne always needs its den.

Watch where the verb lands when the clause contains a Perfekt or a modal: the whole verb block goes to the end, in the usual order. …, die ich gesehen habe · …, das ich kaufen möchte*.