そこで (very rarely seen as 其処（そこ）で) is a combination of そこ ‘there’, and the 格助詞（かくじょし） (case marking particle) で. It is often translated as ‘to that end’, or ‘accordingly’. Literally, it just means ‘at that place’, with で’s use as ‘with’ or ‘by’ highlighting that something will be done there (‘there’ often being a situation). This phrase behaves very similarly to ‘as such’ in English.
Usually, a first sentence will highlight what the ‘situation’ is, before そこで goes on to explain how that situation was or will be resolved.

• 彼（かれ）は雨（あめ）の中（なか）、傘（かさ）なしで立（た）っている。そこで、私（わたし）は車（くるま）から出（で）て彼（かれ）に私（わたし）の傘（かさ）をあげた。
  He is standing in the rain without an umbrella. As such, I got out of the car and gave him mine.
• 彼女（かのじょ）と結婚（けっこん）をすることにした。そこで、彼女（かのじょ）の親（おや）の実家（じっか）に行（い）って挨拶（あいさつ）をすることに決（き）めた。
  I have decided to marry my girlfriend. To that end, I have decided to go to her parents' place to talk to them.
• うちには泥棒（どろぼう）が3回（かい）も入（はい）っている。そこで、防犯（ぼうはん）ガラスを買（か）うことにした。
  Our house has been burgled 3 times already. As such, I have decided to buy an anti-theft window.

As で implies the ‘use’ of something, this expression should only highlight actions that are controllable.

• 信号（しんごう）が赤（あか）になったのでブレーキをかけた。そこで、後（うしろ）ろの車（くるま）に私（わたし）の車（くるま）をぶつけられた。
  Because the traffic turned red, I stepped on the breaks. As such, the car behind me crashed into me.
• 子供（こども）が泣（な）き始（はじ）めた。そこで、子供（こども）に飴（あめ）をあげて落（お）ち着（つ）かせた。
  My kid started to cry. As such, I gave them some candy to calm them down.