Voting in the new country of the United States of America was a slow process. People in rural areas traveled by horse and carriage to cast votes. Each individual state determined how voting was handled. Some cast paper ballots while others used voice votes recorded by county officials according to Colonial Williamsburg's website.
Senators were chosen by electors in each state much like the Electoral College chooses the President. Until the 1850s owning property was seen as the only way to vote in America because leaders feared an illiterate electorate.
Suffrage for former slaves
Only after the Civil War did the United States specifically say who had the right to vote. The 15th Amendment was ratified in 1870 giving former slaves the right to vote. "The right of citizens of the United States to vote shall not be denied or abridged by the United States or by any State on account of race, color, or previous condition of servitude." The 15th Amendment also gave Congress the power to enforce this legislation. It was the first time Congress was given authority to mandate election laws in our history.
Women's voting rights
It was not until 1920 that women were given the right to vote via the 19th Amendment. Congress was again given authority to enforce the Amendment.