Learn Russian: Через месяц они откроют новую мастерскую. - They will open a new workshop in a month.

Мастерская (workshop) is a substantivized adjective: a word that functions as a noun but declines exactly like an adjective. Because it is the direct object of the verb откроют (they will open), it must be in the accusative case. Both the descriptive adjective новая and the noun мастерская change their feminine -ая endings to the accusative -ую.

Why is мастерская a feminine word?

Many nouns that decline like adjectives originally had a regular noun attached to them that was simply dropped over time. Historically, people would say something like мастерская комната (master's room). The feminine noun комната disappeared, but the adjective stayed feminine and became the noun we use today.

Doesn't через usually mean across or through?

It does when talking about physical space! But when paired with a unit of time in the accusative case, через means 'in' or 'after' that amount of time has passed. So через месяц means in a month or a month from now.

Is откроют in the future tense? It looks like it has present tense endings.