(1) Take at least one class with a paper requirement/option. (2) Get to work on the paper right away. (3) Ask the professor in advance if he will give you comments on your paper if you get him a draft early enough, say, by Thanksgiving. (4) Finish a draft paper by Thanksgiving, and give it to the professor for comments. (Don't forget to consult Eugene's book!) (5) Edit the paper based on your professor's comments. If you put some effort into the paper, and paid attention to his comments, you will get a good grade, and very possibly a great grade. (6) Because you have finished the bulk of the work on your paper before Thanksgiving, use the extra time to study for your exams.
And though I titled this post "an easy way to improve law school grades," my experience has been that most law students will write their papers at the last minute, despite all the contrary incentives.