The Constitution established the following guidelines for federal elections:
Although the Constitution established the foundations for federal elections, specific laws and rules that shape the actual voting process and determine who is eligible to vote are created by the individual states. However, the federal government can challenge and sometimes overrule state election policies that it considers unconstitutional.
The following links and videos provide more detailed explanations of federal elections.
When US citizens vote in presidential elections they're actually voting for a group of officials who make up the Electoral College. These people are known as electors and their job is to choose the president and vice-president of the United States.
Each state gets as many electors as it has lawmakers in the US Congress (The Senate and the House of Representatives). California has the most electors (55), while a handful of sparsely populated states like Wyoming, Alaska and North Dakota (and Washington DC) have the minimum of three. There are 538 electors in total. Each elector represents one electoral vote, and a candidate needs to gain a majority of the votes - 270 or more - to win the presidency.
The Constitution created the formal structure of the federal government, and it established the original rules governing national elections. Since its ratification, however, it has been amended numerous times in ways that fundamentally affect national elections. Perhaps the most significant amendments were those that extended the right to vote to populations such as women, African Americans, and people aged 18-21. Other amendments altered the mechanisms by which senators are elected and limited the president to two terms.