Learn French: Regardez en arrière et à droite.

This is a command, which is called the imperative form. When you tell someone to do something, you drop the subject pronoun (vous) and just start with the verb. Regardez here means "Look!" directed at a group or someone you are speaking to formally.

Why do we use the preposition en for en arrière but à for à droite?

Prepositions for giving directions are often set phrases that you simply need to memorize. En arrière is a fixed phrase meaning "back" or "backwards," while à droite is a fixed phrase meaning "to the right." There is no single rule for why they differ; they are just standard pairings.

Since this sentence gives directions, how would I ask "Where do I look?" using the word où?

You could ask Où est-ce que je regarde ? which means "Where do I look?". The word où asks for a location, and the directions in this sentence answer that question perfectly.

What are the opposites of the directions given in this sentence?

The opposite of en arrière (back) is en avant (forward). The opposite of à droite (to the right) is à gauche (to the left).