Learn Dutch: De stad werd door het leger veroverd. - The city was conquered by the army.

In Dutch, an action in the passive voice uses the verb worden (to become), which becomes werd in the singular simple past. Using was (from zijn) would describe a completed state rather than the action itself happening.

Why is veroverd placed at the very end of the sentence?

This is the standard Dutch sentence structure. The conjugated auxiliary verb (werd) sits in the second position of the sentence, while the past participle (veroverd) is pushed all the way to the end.

How do I know whether to end the past participle veroverd with a 'd' or a 't'?

You can use the 't kofschip rule! Take the infinitive veroveren and remove the -en to get the stem verover. Because the last letter is 'r' (which is not a consonant in the word 't kofschip), the past participle ends with a 'd'.

I thought door meant "through". Why is it translated as "by" here?

You're right that door often means "through" when talking about physical movement. However, in passive sentences like this one, door is used to introduce the person or thing performing the action. In this context, it always translates to "by".