Learn French: Elle sort son chargeur de sa valise. - She takes her charger out of her suitcase.

You are exactly right! Usually, sortir means "to go out" (like leaving a building). But when you use it with a specific object that you are moving, it means "to take out". Here, she is taking out son chargeur (her charger), so elle sort translates to "she takes out".

Why does elle sort end in a "t" if sortir is an irregular verb?

Sortir is one of a few common irregular -ir verbs (along with partir and dormir). For the singular forms (I, you, he/she), you drop the -tir from the end. Then you add -s, -s, -t. So for elle, it becomes elle sort.

Why does the sentence use son for the charger and sa for the suitcase, if they both belong to "her"?

In French, words for "his" or "her" match the gender of the object being owned, not the person who owns it. Since chargeur is a masculine noun, we use son. Because valise (suitcase) is a feminine noun, we use sa. Both translate to "her" in this English sentence because she is the one who owns them!

How does de mean "out of" in this sentence?