Learn Swedish: Vi är en familj.

In Swedish, all nouns belong to one of two groups: "en-words" or "ett-words". The word for family, familj, is an en-word, so it takes the article en. You just have to memorize the article when you learn a new word!

Does the verb är mean "are" as well as "am" and "is"?

Exactly! One of the best things about Swedish grammar is that verbs don't change depending on who is doing the action. Whether it is I (jag är), she (hon är), or we (vi är), the verb stays exactly the same.

How do you pronounce the lj at the end of familj?

The letter combination lj makes a sound like the English "y" in "yes". You don't pronounce the "l" or a hard "j". The end of familj just sounds like a soft "y".

Since vi (we) is plural, why is familj singular here?

This works exactly the same way it does in English. Vi refers to multiple people, but together those people make up one single group: en familj (a family).