Learn Russian: Наш сад — за забором.

The preposition за means "behind". When you are describing a static location (where something currently is), за must be followed by the Instrumental case. Since забор (fence) is a masculine noun ending in a consonant, we add -ом to make it забором.

If за takes the Instrumental case here, does it always take the Instrumental?

Not always! If you are describing motion to a new destination (like "we ran behind the fence"), за takes the Accusative case: за забор. You only use the Instrumental case (за забором) for a fixed position, answering the question "where?" rather than "where to?".

Why is there a dash in the middle of this sentence?

The dash takes the place of the verb "is". In Russian, the present tense of the verb "to be" is normally skipped. In writing, a dash is often used to separate the subject (Наш сад) from the rest of the sentence to make it easier to read and to indicate a slight pause in speech.

Should I pause between за and забором when speaking?

No, short prepositions like за are pronounced as if they are glued to the word that follows them. You should flow them together as one smooth word: зазабором.