で (place)
at, in (where something happens)
Place + で + action verb
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で marks the place where an action happens: 図書館で勉強します, "I study at the library"; 家で晩ご飯を食べます, "I eat dinner at home".
Compare に, which marks where something is: 図書館にいます, "I'm at the library". Both are "at" in English, but で goes with doing and に with being. Look at the verb: an action (eat, study, work, play, buy) takes で; あります, います and 住む take に.
Events are the one surprise: 駅で祭りがあります, "there's a festival at the station". Even with あります, an event "takes place", so it's で.
Examples
図書館で勉強します。
I study at the library.
駅前の店で靴を買いました。
I bought shoes at the shop in front of the station.
家で晩ご飯を食べます。
I eat dinner at home.
子どもたちが公園で遊んでいます。
The children are playing in the park.
兄は銀行で働いています。
My older brother works at a bank.