Using ~てしまう to express regret or completion of something

The verb しまう, can be used two different ways. The first is to express completion of something, and the second is to express regret that you did something.
The way to use it in grammar is the same for both uses, so you will have to look at the context of the sentence to figure out the meaning.

しまう is an う verb, so it conjugates like this:
ますform: しまいます
Past form: しまいました
Plain form: しまう
Past plain: しまった
Volitional form: しまおう

When using しまう, you must use a verb in て form in front of it.
Here are some examples:

お酒を飲みすぎてしまいました。
I (regrettably) drank too much.

レポートを書いてしまった。
I finished writing my report.

ノートをわすれてしまった。
I (regrettably) forgot my notebook.

晩ご飯を作ってしまいました。
I finished cooking dinner.

Note: The clause before しまう MUST be something that you have ALREADY done! Even if you are expressing regret, it must be regret about something that has already happened.

Casual form of しまう: ちゃう and じゃう
The casual form of しまう depends on the verb that comes before it.
If the てform ends in て, like 食べて or 買って, then the て+しまう turns into ちゃう.
Examples:
ケーキを食べちゃう。
三十ドルのかばんを買っちゃた。
BUT.
If the て form ends in で, like 飲んで or 読んで, then the で+ しまう turns into じゃう.
Examples:
お酒を飲んじゃった。
本を読んじゃう。