To set up a networking meeting or informational interview, write a request letter/email and then follow up with a phone call if needed. Your letter/email should contain the following information:
Do not send a copy of your resume right away. Your contact will be more likely to help you if you can reassure him/her that you are not looking for a job interview but only for an opportunity to discuss career ideas and obtain some professional feedback about your job search/career goals.
Once you have set up a meeting make sure to come to the meeting prepared. Research the office or organization in advance so you have concrete questions to ask at the meeting. Do not ask the person to explain basic details you could easily learn on your own. The meeting will be more productive if you can ask relevant questions and provide concrete reasons for wanting to pursue a particular career. You also want to make a good impression as he/she will only feel comfortable recommending you to others if he/she feels you will make a strong candidate. Bring a pen and paper so you can write down notes and contact information if needed. During the meeting feel free to ask for suggestions on how to improve your resume to enter the field. At the end of the meeting make sure to ask your contact if he/she can refer you to people who may be helpful to talk to.
Be sure to send a thank you note after your meeting thanking them for their time.