U.S. members of Congress are elected to serve in the U.S. House of Representatives for two year terms. The number of representatives each state is allowed is based on population. At the time of this writing, states are represented by from one to 53 representatives, each of whom represents a geographical district within their state. Article II, Section 2, Clause 4 of the U.S. Constitution dictates that a state's governor must call for an election to fill any vacancy in the House of Representatives, including vacancies caused by a resignation.
Wait for your governor to issue a writ of election for the vacant congressional district. After this writ is issues, the full election process, including primaries for all nominating parties, will take place. In most cases, the election process takes between three to six months.
Participate in the primary process of the political party of your choice. In some states, you are allowed to participate in the primary process even if you are not a member of the political party in question. Members of a political party are always allowed to participate in the nomination process for congressional candidates of their party.
Vote when the election is scheduled. Your governor may call for a special election or may wait and have the election held during the next general election. In most cases, a special election will be called if the vacancy could be filled in time for the new member of Congress to participate in a session of Congress before the next general election.
Contact your congressional district's interim office or the office of the nearest congressional district with a sitting representative if you need any of the services normally provided by your member of Congress while your congressional district is without representation. Vacant congressional district offices may advise you regarding the status of any legislation before the U.S. Congress, but may not offer commentary or opinion on the legislation.
Be aware that your congressional district will be unrepresented in the House of Representatives until a new member of Congress is elected to represent you. If you don't feel that the special election is being handled in a timely manner, contact your governor's office to express your concern.
Unlike U.S. Representatives, resigning senators may often be replaced by appointment. Some states' laws dictate a special election for Senate vacancies. Other states' laws allow the governor to appoint a senator who serves until the next scheduled election for that Senate seat.