Research your legislator's history. Develop a strategy for the meeting. Decide who will speak, for how long, and on what issues. Focus on what you want your legislator to do. Bring local data to support your arguments - data relevant to the legislator's district and key constituencies, if they are available.
Politicians tend to speak generally and go off on tangents.
Don't let them. Try to politely draw out specific answers to specific questions. Don't be afraid to admit ignorance on specific points. Say you will do your best to get the answer and will report back. Immediately after the meeting, make notes on what was discussed and what the legislator agreed to do.