Learn Spanish (Spain): Vamos a buscar un postre barato. - We are going to look for a cheap dessert.

In Spanish, the verb buscar means "to look for" all by itself. You do not need to add a word like por or para after it. So, "to look for a dessert" is simply buscar un postre.

How does vamos a work here to mean "we are going to"?

This is a very common way to talk about the future in Spanish. You combine a form of the verb ir (to go) + a + an action verb in its basic form. Since vamos is the "we" form of ir, vamos a buscar translates to "we are going to look for".

Why is there no word for "we" at the beginning of the sentence?

The word vamos already means "we go" or "we are going". Because the verb itself tells you exactly who is doing the action, Spanish speakers usually drop the word for "we" (nosotros) unless they want to add special emphasis.

Why is barato placed after postre?

In Spanish, descriptive words (adjectives) usually come right after the thing they are describing. Instead of saying "cheap dessert" like in English, you flip the order and say "dessert cheap" (postre barato).