Learn Russian: Летом мы часто готовим шашлык на даче. - In summer we often make shashlik at the dacha.

In Russian, seasons and times of day often use the instrumental case without a preposition to answer the question "when?". Лето is the dictionary word for summer, and летом is its instrumental form, meaning "in the summer".

Why do we use the preposition на for на даче (at the dacha) instead of в?

The word дача historically implies a piece of land or an estate, so it is treated as an open space or territory. In Russian, we use на for open spaces and events, so you must always say на даче (at the dacha, in the prepositional case) and на дачу (to the dacha).

Why is шашлык in the singular form here? Doesn't a barbecue involve multiple skewers of meat?

While it can be plural (шашлыки) to mean the social event of having a barbecue, the singular шашлык is commonly used as an uncountable mass noun to refer to the food itself. Here, it is in the accusative case because it is the direct object being cooked. It looks exactly like the nominative case because it is an inanimate noun.

The English translation says "make shashlik", but doesn't готовим mean "cook" or "prepare"?

Yes! The verb готовить means to cook or prepare food. Russian relies on this verb for creating meals instead of делать (to do/make), which is why you shouldn't translate "make shashlik" word-for-word.