Brush up on punctuation rules from a simple guide, such as Strunk & White's "The Elements of Style."
Look for missing punctuation. Editing for punctuation is about find what's missing as well as changing what's wrong. Look for run-on sentences that need to be divided with periods and quotations that are missing quote marks.
Look for mistakes with commas. While there is no absolute set of guidelines for all the uses of commas, some, such as placing a comma between two independent clauses joined with a conjunction, are the same for all English grammar styles. Other comma rules are regional, but still indelible within those regions. In the U.S., for example, you must always place commas within closing quotation marks, while in UK you need not.
Check all punctuation marks that are commonly interchanged (wrongly) with other punctuation marks, such as colons and semicolons, and dashes and hyphens. There are dozens of Internet resources for determining the different uses of commony interchanged punctuation marks. To find them, do an Internet search for phrases such as "colon vs semicolon."
Remove excess exclamation points and ellipses. Nonessential exclamation points and ellipses will make writing appear less professional. Use exclamation points only when absolutely necessary for emphasis, and use ellipses only to show that a thought, quote or phrase has been cut off before it is finished or has been begun in the middle.
Refer to any particular style guides you are to follow, and use their guidelines first and foremost. Often, there are "house rules" for grammar that you must follow when editing. Other times a style guide such as the Associated Press Style Guide or the Chicago Manual of Style is assigned by a school, employer or institution.
Once you think you have corrected the punctuation in a document appropriately, read the entire thing aloud, pausing for commas and periods. This will help you make sure that sentences flow and that commas are placed appropriately, and it will help you catch mistakes that your eye may have missed when reading silently.