Learn German: Wir haben dreizehn Äpfel gekauft.

It combines drei (three) and zehn (ten). Just like English 'thirteen', German numbers from 13 to 19 are built by putting the single digit first, followed by zehn.

How does the singular Apfel change to the plural Äpfel?

To make Apfel plural, you don't add an 's' like in English. Instead, you just add an umlaut (the two dots) over the A. This changes the pronunciation from an 'ah' sound to an 'eh' sound.

Why is gekauft at the very end of the sentence?

This is a strict rule for the spoken past tense in German. The helping verb (haben) takes the normal second position, but the main action word (gekauft) gets pushed to the very end. You are literally saying, 'We have thirteen apples bought.'

How does the verb kaufen (to buy) become gekauft?

Most regular verbs in the past tense are built by adding ge- to the beginning and -t to the end of the verb stem. Take the stem of kaufen (which is kauf), add those pieces, and you get ge-kauf-t.