This is the easiest and fastest part of the process. Once you have your second draft completed it's time for some peer editing. After the rough draft I suggested you have someone who's in the same course and/or writing a similar kind of paper to peer edit because they may be able to help you construct clearer sentences since they have more background information on the topic.
After your second draft is completed have a friend who is not in your class edit the paper. Better yet, bring you r paper to your college writing center or your TA for the class. They love to help students edit their papers because it shows them that your trying, plus they can provide amazing insight!
Once you get your edited draft returned read through it and make the appropriate changes. The final step is to go back to the assignment. Make sure you have completed every portion of the asked assignment. Make sure you have answered the question asked of you completely and correctly. Make sure you directly supported your thesis throughout all aspects of your paper.
Once you have cross referenced everything and you're happy with your paper than you're done! That's it. You've successfully written a college paper without completely losing your mind.