Learn German: Die Kinder essen die Kirschen. - The children are eating the cherries.

German doesn't have a continuous tense like English does. Whether the children "eat" generally or "are eating" right now, you just use the standard present tense verb essen. Never try to say sind essen!

Are both instances of die doing the exact same job here?

Not quite! The first die is in the nominative case because die Kinder are the subject (the ones doing the eating). The second die is in the accusative case because die Kirschen are the direct object (the things being eaten). Fortunately, the plural word for "the" is die in both cases, so it looks identical.

How can I tell that Kinder and Kirschen are plural?

German plurals have a few different endings. Kinder (children) comes from the singular das Kind and adds -er. Kirschen (cherries) comes from the feminine singular die Kirsche and adds an -n. The article die before both of them is also a strong clue that they are plural.

I thought the verb essen was irregular. Why does it just look like the normal dictionary form here?

You're right that essen is a strong (irregular) verb, but its vowel changes usually only happen in the singular forms, like er isst (he eats). In the plural forms like wir essen and sie essen (they eat), it goes back to looking exactly like the infinitive base verb.