Be punctual and polite. Be on time, and thank the staff person for his or her time. You may not agree with your members of Congress on every issue, but you can absolutely present an argument clearly and passionately without hostility.
Be passionate. It is important to speak with your Member's office with gumption. There is some reason that you feel strongly about the issue and wanted to hold the meeting, so do not be afraid to share!
Be personal. Remember that you do not have to be an expert on an issue; members of Congress meet with you because you elect them, and they care why these issues are important to you.
Be persuasive. Give several brief points about why your Member of Congress should support or oppose certain legislation, and be concrete and clear. Rather than something generic like "I want you to support the environment," a more effective ask is to support a specific bill or legislative action: "I would like Congressman Smith to support H.R. 5432, the Tree Planting Act."