Section 4: Congressional elections
Clause 1: Time, place, and manner of holdingThe Times, Places and Manner of holding Elections for Senators and Representatives, shall be prescribed in each State by the Legislature thereof; but the Congress may at any time by Law make or alter such Regulations, except as to the Places of chusing [sic] Senators.
This clause generally commits to the States the authority to determine the "times, places and manner of holding elections," which includes the preliminary stages of the election process (such as a primary election), while reserving to Congress the authority to preempt State regulations with uniform national rules. Congress has exercised this authority to determine a uniform date for federal elections: the Tuesday following the first Monday in November.
Because Congress has not enacted any on-point regulations, States still retain the authority to regulate the dates on which other aspects of the election process are held (registration, primary elections, etc.) and where elections will be held. As for regulating the "manner" of elections, the Supreme Court has interpreted this to mean "matters like notices, registration, supervision of voting, protection of voters, prevention of fraud and corrupt practices, counting of votes, duties of inspectors and canvassers, and making and publication of election returns." The Supreme Court has held that States may not exercise their power to determine the "manner" of holding elections to impose term limits on their congressional delegation.
One of the most significant ways that States regulate the "manner" of elections is their power to draw election districts. Although in theory Congress could draw the district map for each State, it has not exercised this level of oversight.
Congress has, however, required the States to conform to certain practices when drawing districts. States are currently required to use a single-member district scheme, whereby the State is divided into as many election districts for Representatives in the House of Representatives as the size of its representation in that body (that is to say, Representatives cannot be elected at-large from the whole State unless the State has only one Representative in the House, nor can districts elect more than 1 Representative).