Learn German: Wir haben zehn Finger.

In German, masculine and neuter nouns that end in -er, -el, or -en usually don't add a new ending in the plural. Some get an umlaut (like der Bruder becoming die Brüder), but der Finger stays exactly the same: die Finger.

How can I tell if Finger is singular or plural if the word itself doesn't change?

You have to look at the context words around it. In this sentence, the number zehn (ten) makes it clear we are talking about more than one. In other sentences, look at the articles or adjectives, such as mein Finger (singular) versus meine Finger (plural).

Are there other German body parts that follow this same plural rule?

Yes! Other masculine body parts ending in -en or -er work the same way. For example, der Daumen (the thumb) becomes die Daumen and der Rücken (the back) becomes die Rücken.