Electing the President & Vice - The U.S. Election Process
This is a multiple step process: local nominations in the states, followed by the national convention nomination in summer, when the two major parties nominate their major candidate, then the general election campaign when every candidate seeks to convince voters, and the electoral college phase, the final step to deternine the new president.
Either a candidate must be nominated by his party or the candidate can be an independent one without party affiliation.
Anyhow, whether representing a party or not, it is an expensive way to run for the presidency. About 12-18 month before the election the candidates start their fundraising rally.
Approximately at the time when the term of the current president is half over, that means about 2 years after the election, the media begin to ask who the next challengers will be. So possible candidates come up, but still need an O.K. from their party, if there is one behind them. That'll be called the nomination process, the primaries.
Primaries on state level
First on a state level to reduce the field of candidates. That starts approximately in February of the election year.
But normally also on the nation level, because running for president means to be popular person, loved by the media, by the voters, by anyone. The media play a huge role during the entire process. Candidates present themselves, are literally x-rayed by opponents, who try to find the little black spot in the candidate's past to ruin his or her campaign.
Primaries on nation level
The big national Conventions of the two major parties, the Democrats and the Republicans, usually take place during summer of the election year.