Learn Hardcore Polish: Zamieszaj proszę herbatę łyżką.

It’s the 2nd person singular imperative of the perfective verb zamieszać. Using the perfective here asks for a single, completed action: “Give it a stir.” By contrast, Mieszaj! (imperfective) means “Keep stirring!” or “Stir continuously.”

Why is it herbatę and not herbata?

Herbatę is the accusative singular of the feminine noun herbata. Accusative marks the direct object of a transitive verb: you’re stirring the tea. The common -a > -ę change in the accusative is typical for feminine nouns (e.g., kawa → kawę, zupa → zupę).

Why is it łyżką? What case is that?

Łyżką is instrumental singular of łyżka. Polish uses the instrumental case to express the means/instrument used to perform an action, often without a preposition: “(stir) with a spoon.” Feminine -a nouns take -ą in the instrumental: łyżka → łyżką.

Could I say z łyżką instead?

Not for the tool meaning. Z łyżką usually means “with a spoon (together/alongside),” i.e., accompanied by a spoon, not using it as a tool. To express “using a spoon,” the bare instrumental łyżką is the natural choice.

Where can I put , and do I need commas?