Collect all the letters and mail them off that day. This approach will take a little more energy from the participants, so show your enthusiasm and get everyone excited. Your purpose for writing should be stated in the first paragraph. This way, they know what you're talking about. Include how the proposed legislation or issue affects you personally.
Anecdotal evidence is a an effective and persuasive lobbying tool.
Offer your expertise if it is relevant. Believe it or not, as a medical student you may have experiential or trained expertise that may be useful to legislators. These people are not experts on all issues. Always ask the senator or representative for something. Always thank the senator or representative for something.