Because the hiragana ends with an う sound, you know this word is a verb. The kanji itself means worry so the verb vocab version is to worry.

悩む is often intransitive, like 彼はいつも悩んでいる (he's always worrying). But it can also be transitive, in which case it'll take a direct object, like 彼女のことを悩む (to worry about her).

The reading is the same as what you learned with the kanji, so no need to worry about it.