There are no constitutionally mandated rules, OE. Article IV, Section 4, reads, in its entirety:
The United States shall guarantee to every State in this Union a Republican Form of Government, and shall protect each of them against Invasion; and on Application of the Legislature, or of the Executive (when the Legislature cannot be convened) against domestic Violence.
Therefore, each state more or less mimicks the central government in the composition of its government. In the states, the office of Secretary of State concerns itself with management of governance in the state (after all, none of the states are sovereign to conduct and independent foreign policy, so the office is going to vary crucially from the Federal State Department)--and acts as a controlling agency and liaison with the lower levels of government, the counties or parishes and the municipalities. That can vary from state to state as well--for example, when i lived in Virginia, municipalities were independent of the government of the counties in which they were located (and i believe this is still so).
The states have tended, especially since the Civil War, to follow the lead of the Federal government (or to do the direct opposite, as was often the case with southern states before the 1960s) in their governance. Most state constitutions mirror the United States Constitution, and concern themselves with higher degrees of civil rights than provided for in that document, and with details of state and local governance. All of the states must have a care not to violate the due process provision of the XIVth amendment, which also guarantees equality of civil rights to all citizens of the several states. Beginning in the 1880s, states have amended or re-written their own constitutions to assure that their citizens have the minimum of civil rights which are based on the United States Constitution, and that there are appropriate mechanisms and oversights to assure this. Additionally, in the last century, states have accorded to their citizens civil rights which the Supremes have declared only apply the relationship between citizens and the Federal government (many times the Supreme Court has determined that a particular provision applies only to the Federal government--so states have taken measures to assure those civil rights to their citizens).
Therefore, even when voting rights acts which only concern themselves with national elections have been passed, the states have been quick to enact similar measures. The states will act independently, of course, in matters which are soley within their own perview, but they are prone to adopt the simplest most effective governance measures which have become common among the several states. Many amendments and Federal laws govern voting, leaving states with little room to innovate or diverge from a standard practice. The XVth Amendment prohibits racial discrimination in voting. The XVIIth Amendment established popular election as the sole method for choosing United States Senators (previously, the states were free to choose or appoint Senators as they saw fit--although this amendment was ratified in 1913, many states had already passed measures for the popular election of Senators), and many states made a great many offices, therefore elective, which is why state Secretaries of State are elected officials. The XIXth Amendment gave women the vote, and once again, the Federal government lagged behind some of the states which had already enacted women's suffrage. The poll tax was not prohibited until the XXIVth Amendment was ratified in 1964, which was just one voting rights measure which grew out of the civil rights movement in the American south in the 1960s.
And that is the era from which a large measure of standardization arises in voting regulations in the United States. Any state or local government which violated the
1965 Voting Rights Act would be a prime target for ruinous litigation--it was the measure which broke the back of Jim Crow in the South. It has been extended by new measures in 1970, 1975 and 1982. As has been so common in the history of state legislation and constitutions, the states have since then quickly moved to assure that they won't be embarrassed by the glare of publicity about voting rights and procedures in their jurisdictions. This is why people (who weren't lock-step Bush supporters) were scandalized by the shenanigans of Katherine Harris in Florida before the 2000 election, when she was Secretary of State, and tens of thousands of (mostly African American) voters were stricken from the rolls based on the unsubstatiated report of a private business which had contracted to investigate the registration rolls--and many of those who thought it a bad thing had voted for Bush.
So, although each state determines the nature of its ballot, and what machines, if any, are used in the voting--the basic procedures, and guarantees of voting rights, are standard by a default consensus. Finally, in 1975, the
Federal Election Commission was created to administer the implementation of the Federal Campaign Finance Act, and the states have been quick to introduce and enforce their own, internal campaign finance legislation.
If you do a web search for "State Board of Elections," you'll get hits for every one of the fifty states, and many hits which link directly to the web sites of the Secretaries of State of the various states. Additionally, state constitutions can easily be found online.
