During my German lessons students tend to meet the Perfekt, grow comfortable with it, and then run into a sentence that places one past event before another. That is the job of the Plusquamperfekt, the German past perfect. It is one of the easier tenses to form, and one of the easiest to place correctly once you know the single word that usually triggers it.
How the Plusquamperfekt is formed
The formula is the Perfekt with the auxiliary moved one step further back in time. Instead of the present tense of haben or sein, you use the simple past, hatte or war, followed by the past participle at the end of the clause.
Ich habe das Buch gelesen. I have read the book.
Ich hatte das Buch gelesen. I had read the book.
Wir sind angekommen. We have arrived.
Wir waren angekommen. We had arrived.
The participle itself does not change. If you can already form the Perfekt, you can form the Plusquamperfekt.
hatte or war?
The choice of auxiliary follows exactly the same rule as the Perfekt. Most verbs take haben. Verbs that convey movement from A to B or a change of state take sein, as do sein, bleiben and werden themselves.
Er hatte den Vertrag unterschrieben. He had signed the contract.
Er war nach Berlin gefahren. He had travelled to Berlin.
When you actually need it: nachdem
In practice, most of the Plusquamperfekt you will meet in German follows nachdem (after). German is stricter here than English. Where an English speaker might say “after I finished the report, I went home”, German expects the earlier action in the Plusquamperfekt and the later one in the simple past.
Nachdem ich den Bericht geschrieben hatte, ging ich nach Hause.
Note the word order. Nachdem introduces a subordinate clause, so the conjugated verb moves to the very end, after the participle. In a main clause you would say hatte geschrieben; here it becomes geschrieben hatte.
The same logic applies after als and bevor:
Als wir ankamen, war der Zug schon abgefahren. When we arrived, the train had already left.
Plusquamperfekt or Perfekt?
Use the Perfekt when you are simply saying that something happened. Reach for the Plusquamperfekt only when you need to show that one past event came before another past event. If there is no second point of reference in the past, you do not need it.
Ich habe in München gewohnt. I lived in Munich, as a plain fact about the past.
Ich hatte in München gewohnt, bevor ich nach London zog. I had lived in Munich before I moved to London.
hatte or hätte?
This is where I correct most mistakes. A single umlaut separates the past perfect from the Konjunktiv II in the past:
Ich hatte es gewusst. I had known it, and it happened.
Ich hätte es gewusst. I would have known it, and it did not happen.
The same applies to war and wäre. Reading the umlaut carelessly reverses the meaning of the sentence, so those two vowels repay a little care.
If you would like to work through tenses like this with a native tutor, private German lessons in London cover exactly this kind of distinction.