Learn Hardcore Japanese: watasiha mise de kutu wo yasuku kaimasita.

The particle で marks the location where an action takes place. Here, 店で means “at the store,” showing that the buying happened in that place (not “to” the store, which would use に).

What is the function of the particle を in 靴を買いました?

The particle を marks the direct object of the verb. In 靴を買いました, 靴 ("shoes") is what you bought, so を indicates what is being acted upon by 買いました.

Why is 安く used instead of 安い?

安く is the adverbial form of the adjective 安い. To modify a verb like 買いました, you need an adverb (安く “cheaply”), not the adjective itself.

Why does 買いました appear at the end of the sentence?

Japanese follows a Subject–Object–Verb (SOV) order, so the verb always comes at the end. You say ～靴を買いました (“bought shoes”) rather than “I buy shoes did.”

What role does は play in 私は?

The particle は marks the topic of the sentence. 私は sets “I” as the topic (“as for me”), indicating that the rest of the sentence provides information about you.

How do you turn an い-adjective like 安い into an adverb?

For い-adjectives, drop the final い and add く. So 安い (cheap) becomes 安く (cheaply).

Can I move 安く to a different position in the sentence?

Yes. As long as it comes before the verb, you can place it closer to the beginning:
私は店で安く靴を買いました. It still must precede 買いました.

Could I say 安い靴を買いました instead, and what's the difference?

Yes. 安い靴を買いました means “I bought cheap shoes,” directly describing the shoes as cheap. 安く買いました emphasizes that you bought them at a low price (the manner of buying).

What does the ending ました on 買いました indicate?

ました is the polite past-tense ending for 買う (“to buy”). It shows the action is completed in the past and adds politeness. The plain past is 買った.