Try a beginner strategy of evaluating one sentence at a time for its punctuation: “The report was finished, however it was not sent.” Such a sentence looks nearly fine on a quick read-through because the words are common and the sense is transparent; the punctuation problem is between the independent clauses. Evaluating one sentence at a time can help you slow down enough to consider boundaries that meaning alone would sweep past.
Take a small section of a text, and view each sentence by itself by covering the rest of the text with a piece of paper, using a ruler, or employing an on-screen feature that displays only that sentence. Read the sentence aloud, then locate its beginning and ending. How many independent clauses are present? Focus only on the punctuation; there will be separate, later checks of spelling and style (except when such errors obscure meaning). Examine each mark, comma, period, semicolon, colon, apostrophe, quotation mark, bracket.
What task is each one performing? A comma separates a list, or shows a pause after an introductory phrase or between an independent and a dependent clause. An apostrophe shows possession or missing letters; quotation marks identify spoken language or a cited phrase. Identify each function to make the checking more consistent than judging marks as “correct by feeling.”
Pay careful attention to sentence boundaries. Joining two independent clauses with just a comma (a comma splice) is incorrect. An independent clause by itself (a sentence) may be incorrect as well. A long sentence (or one with multiple independent clauses) may require a different type of connection, but changing the structure is not proofreading. If there seems to be more than one possible correction for a sentence, query it rather than risk an incorrect change.
Often beginning proofreaders look for only the punctuation where they hear natural pauses in speech. Rhythm in speaking can be helpful but is not the whole rule: some correct commas produce little change in rhythm, and some rhythm pauses need no punctuation. The choice may also be affected by house style in regard to lists, quotations, introductory words and phrases. Note your consistent decisions, and add any unusual cases to a consistency sheet.
When you have made your changes and are checking a clean copy, read aloud the revised text again, checking each punctuation mark against the original to confirm that no duplicate or missing or misplaced change has been made. Finally, ask yourself about each change: do you know the function of this mark in this sentence? If so, you can have more confidence in your correction.