Learn German: Wir wandern vierundzwanzig Kilometer. - We are hiking twenty-four kilometers.

In German, numbers from 21 to 99 are said "backwards" compared to English. You say the ones digit first, then und (and), then the tens digit. So 24 is vier (four) + und + zwanzig (twenty), making vierundzwanzig.

Is vierundzwanzig really written as one long word without spaces or hyphens?

Yes! In German, compound numbers smaller than one million are written together as a single, long word. You won't use spaces or hyphens like you do in the English "twenty-four".

Why does Kilometer look singular here? Shouldn't it have an "s" at the end for plural since there are twenty-four of them?

In German, masculine and neuter units of measurement usually don't change their ending in the plural when they come directly after a number. Because it is der Kilometer (a masculine word), it stays exactly the same whether you are hiking one or twenty-four of them.

Why doesn't the verb wandern end in "-en" like other verbs used with wir?

The dictionary form of "to hike" is actually wandern, ending in "-ern" rather than the typical "-en". Since the wir (we) form of a verb is almost always identical to its dictionary form, it simply stays wandern.