Legislators and their staff communicate with constituents regularly. It is very common to request an appointment with your legislator in his or her Austin or home district office. If you meet with a staff person instead of a Member, be aware that he or she serves as a liaison to the Member and often briefs the Member on these issues. Know the legislation relevant to the issue you wish to discuss. You should be able to provide a brief, nonscientific explanation of the issue, avoiding jargon, acronyms, etc.
Legislators have hectic and unpredictable demands on their time.
It is important to follow your own style. But, a suggestion for initiating the conversation, is to tell the legislator a little bit about yourself, what you study, why you choose to study it, why you choose to study it here, and what you do in a day. Then let them know what would make your life as a graduate student easier. Follow up Follow up the appointment with a thank-you letter summarizing the key points of your visit. Keep it to one page.