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Contact the right level of government. Don’t call Congress about your city sidewalks, don’t call your state representative about the Affordable Care Act, and don’t call the city about education funding.
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Contact your own legislator and include your address. If you really want to target another legislator (chair of a key committee, for example), organize your friends and relatives who live in that district to contact them. Out of district contacts are ignored.
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Be specific, polite, and brief. No need to get into a long explanation of why you do or don’t support the issue-- staff should already be familiar with it. Stick to one issue at a time.
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Email, call, or go in person to a townhall. Members of Congress attend lots of community and party functions where you can say a few words to them (Labor Day picnics, MLK Day celebrations, etc). You can also request a face-to-face meeting with a legislator or their staff, especially if you organize a whole group of people. Don’t be shy-- the worst that can happen is they say they are busy.
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Faxes and paper letters are better than nothing, but less likely to get a timely response.
Edited to add: 6. Understand who controls what. Unless your legislator is the committee chair for the bill, they can’t schedule a hearing on it. They can ask the committee chair to do that, but that isn’t likely to help if the chair is from the other party. Likewise, only the Speaker can bring a bill up for a vote on the House floor-- and is not likely to listen to minority members in setting those priorities. At a minimum, check which party your legislator belongs to and which party holds the majority in the state or federal legislative chamber they belong to. Committee chairs belong to the majority. Otherwise, you will not have a realistic picture of where to apply pressure.