Learn Arabic (Modern Standard): دخلوا الحرب أمس.

The suffix for "they" in the past tense is ـوا (waw followed by an alif). This alif is completely silent. It acts as a spelling marker used at the end of verbs to show that the "waw" is a plural ending, rather than a core letter belonging to the root of the word itself.

Where is the word for "they" in this sentence?

The pronoun "they" is built directly into the verb! The base form is دخل (he entered), and adding the plural suffix ـوا changes it to "they entered". Because the suffix already tells us exactly who did the action, you don't need to add the separate pronoun هم (they).

In English we sometimes say "entered into the war", but is there a missing preposition here?

No preposition is needed here. In Arabic, the verb دخل (to enter) connects directly to its object. You simply say "entered the war" (دخلوا الحرب) without adding any Arabic word for "in" or "into".

How do we pronounce the word for "yesterday" (أمس)?

In formal Modern Standard Arabic, it is typically pronounced "amsi" with a short "i" sound at the end, regardless of its position in the sentence. However, because it falls at the very end of this sentence, it is completely normal to pause and drop that final vowel, pronouncing it simply as "ams".