Learn Dutch: Geniet je van de vakantie? - Are you enjoying the vacation?

You are right that van usually means "from" or "of". However, the Dutch verb for "to enjoy" is genieten van. This is a fixed preposition, meaning the verb and preposition always go together when you mention what you are enjoying.

Doesn't the verb lose the "t" when je comes after it in a question? Why is it still geniet?

You do drop the extra "t" when je or jij follows the verb. But the stem (the core part) of the verb genieten is geniet. Because the "t" belongs to the stem itself and isn't an extra added letter, it stays.

The English translation says "Are you enjoying". Why don't we use the Dutch continuous form with aan het?

Dutch uses the simple present tense much more often than English. While you could say Ben je van de vakantie aan het genieten?, the simple form Geniet je... is perfectly natural and the most common way to ask this.

How do I know whether to use de or het with vakantie?

Vakantie is a de word. A helpful trick to remember is that almost all Dutch words ending in -ie (like politie, familie, and vakantie) use de.