〜てしまう

Verb て-form + しまう (casual contraction: て-form + ちゃう, で-form + じゃう)

• 電車の中で財布を落としてしまった。

  でんしゃのなかでさいふをおとしてしまった。

  I dropped my wallet on the train, much to my dismay.

• このレポートを今日中に書いてしまいます。

  このレポートをきょうじゅうにかいてしまいます。

  I will finish writing this report by the end of today.

• 大事な用事を忘れてしまわないように、メモしておきます。

  だいじなようじをわすれてしまわないように、メモしておきます。

  I'll make a note so that I don't end up forgetting the important errand.

• え、もう食べてしまったの？

  え、もうたべてしまったの？

  What, you already finished eating it?!

• 全部終わってしまいましたか。

  ぜんぶおわってしまいましたか。

  Has everything already finished?

• うっかり秘密を言っちゃった。

  うっかりひみつをいっちゃった。

  I accidentally let the secret slip out.

• 気をつけないと、また同じ失敗をしてしまいますよ。

  きをつけないと、またおなじしっぱいをしてしまいますよ。

  If you're not careful, you'll end up making the same mistake again.

• Assuming てしまう is always negative or regretful — while it very often carries regret, it can also simply emphasize that an action is completely finished with no negative feeling at all, e.g. 宿題は全部やってしまいました can mean 'I finished all my homework' with relief; the nuance must be judged from context, not assumed automatically.
• Confusing the independent verb しまう ('to put away / store') with the auxiliary 〜てしまう attached after another verb's て-form — these are different usages; the auxiliary must attach to the て-form of the main action verb (e.g. 財布を落としてしまった), not stand alone as if しまう itself were the main action being described.
• Forgetting that the casual contractions follow the て/で-form voicing rule: verbs whose て-form ends in で use じゃう, not ちゃう, so 飲んでしまう becomes 飲んじゃう (not 飲んちゃう); verbs whose て-form ends in て instead use ちゃう, so 走ってしまう becomes 走っちゃう (not 走っじゃう).

〜ておく (do in advance / leave in a state for later benefit)

ておく expresses doing something in advance, in preparation for the future, with a purposeful, forward-looking nuance: 旅行の前に荷物を準備しておきます (I'll pack my luggage in advance before the trip). てしまう expresses that an action is completed entirely, often about something that has already happened, with a nuance of regret or an unintended result: 準備しないで、旅行に行ってしまいました (I went on the trip without preparing, and I regret it) — the focus is on the completed, often unwanted result, not on preparing ahead of time.

verb stem + 終わる (finish ~ing)

動詞の連用形+終わる (e.g. 食べ終わる 'finish eating', 書き終わる 'finish writing') simply states that an ongoing action has reached its physical or time completion, with no emotional coloring at all: レポートを書き終わりました (I finished writing the report) is a plain, neutral fact. てしまう also marks completion, but often adds a nuance of regret, surprise, or an unintended/uncontrollable result (the exact feeling depends on context, and it can also be neutral or relieved), and unlike 終わる it can attach to instantaneous, one-moment verbs too: 財布を落としてしまった (I dropped my wallet, much to my dismay) is natural, but 財布を落とし終わった is unnatural because 落とす ('to drop') has no ongoing duration to finish. Compare 宿題をやり終わった (I finished doing my homework — a plain, neutral fact) with 宿題をやってしまった (I got all my homework done — depending on context, this can add relief at finally being done, or a hint of resignation/surprise).

N4 grammar sections frequently test てしまう by having students distinguish it from plain past tense or from ておく in sentences implying regret, surprise, or an accidental/uncontrollable outcome; listening sections often use the casual contractions ちゃう/じゃう in natural conversation, so recognizing them quickly is also tested.