Start with Problem Areas
When proofreading, look first for those problems you know you have. If you know you make errors with sentence punctuation, check all sentences for completeness first. For instance, many proofreading errors involve using commas where semicolons are required. As a separate proofreading step, look at each sentence in your final drafts. Check that any commas in the middle of sentences aren't separating two sentences that could otherwise stand alone. If you have just a comma between what could be two sentences, change that to a semicolon.
Then read the paper again for each problem teachers have suggested you work on. You may have to look at the paper five or six times to be thorough, so try splitting up your proofreading. Check for sentence punctuation and one other problem in one sitting, and then come back after a break to look for other problems.