Learn Russian: Ей легко найти общий язык с детьми. - She finds common ground with children easily.

Exactly. The Russian idiom найти общий язык literally translates to "find a common language." It is the standard way to say you have established a good rapport, reached an understanding, or found common ground with someone.

Why does the sentence use the dative Ей instead of the nominative Она?

This is a classic Russian impersonal construction. Instead of saying "She finds it easy" (an active subject doing an action), Russian phrases it as "To her, it is easy" using the dative pronoun ей followed by the adverb легко. This is the most natural way to express how someone experiences a state or level of difficulty.

Since this is a general, ongoing ability she has, why use the perfective verb найти?

When talking about a potential or ability to get something done, Russian often uses the perfective aspect to focus on the successful result. Using the perfective найти emphasizes that she consistently achieves that connection. The imperfective находить would also be grammatically correct but would shift the focus to the ongoing process of trying to connect.

Is с детьми an irregular instrumental plural form?

Yes! The nominative plural is дети (children), but its instrumental form is детьми rather than taking a standard ending. This is a leftover from an older declension class. You will see this exact same irregular -ьми ending on the word люди (people), which becomes с людьми (with people).