Make sure to write a thank you card or send a thank you email to the person you met with during the meeting. When you build a relationship with staffers, they are more likely to prioritize your issues. Be aware: due to security precautions, there is a lengthy process to ensure all mail sent to government buildings does not carry any contamination. Email is always best, especially if the issue is time sensitive (for example, an upcoming vote).
Respond via email to any questions that you were unable to answer at the meeting. Alternatively, schedule a follow-up meeting if the questions were extensive and you would like to speak more about them in person.
Suggest that the staffer/member attend upcoming briefings/hearings related to your cause (do research and provide dates/times of suggested briefings/hearings).