war, hatte, konnte, musste

You already have one past tense: the Perfekt (ich habe gearbeitet). In spoken German that is the normal past for almost every verb. But there is a small group where speakers almost never use the Perfekt — they use the Präteritum, the simple past, instead.

sein, haben and the modals → Präteritum. Everything else → Perfekt.

That is the whole rule at this level. Ich bin müde gewesen is not wrong, but it sounds heavy; every German says Ich war müde.

ich and er/sie/es are identical — war, hatte, konnte. No -e, no -t.

That shared form is the single most useful thing to remember. Ich war and er war; ich hatte and sie hatte. In the present you learned ich bin / er ist; in the Präteritum the two collapse into one.

The modals lose their umlaut: können → konnte, müssen → musste, dürfen → durfte. Only wollen and sollen had none to lose, so they simply add -te.

• Ich war gestern müde.

  I was tired yesterday.

• Ich hatte keine Zeit.

  I had no time.

• Ich konnte nicht kommen.

  I could not come.

  modal second, infinitive at the end — exactly as in the present

• Ich musste arbeiten.

  I had to work.

• Ich wollte früher gehen.

  I wanted to leave earlier.

• Wir durften nicht parken.

  We were not allowed to park.

Notice that the sentence structure has not changed at all. A Präteritum modal sits in position 2 and pushes its infinitive to the end, just like ich kann kommen → ich konnte kommen. You are swapping one word, not learning a new word order.

Compare the two pasts side by side. Both sentences below are about yesterday; the difference is only which verb is involved.

• Gestern habe ich viel gearbeitet.

  Yesterday I worked a lot.

  arbeiten → Perfekt

• Gestern hatte ich viel Arbeit.

  Yesterday I had a lot of work.

  haben → Präteritum

• Ich bin nach Berlin gefahren, aber ich hatte kein Ticket.

  I went to Berlin, but I had no ticket.

  both tenses in one sentence, each with its own verb

sollte is worth a separate note. Ich sollte arbeiten usually means I was supposed to work — and in the present it is also the polite "should": Du solltest schlafen. Both come from the same form, so you get two uses for one word.