Every four years since 1996, the Green Party nominates its presidential and vice-presidential candidates at its quadrennial Presidential Nominating Convention. In 2016 the Green Party of the United States convention will be in Houston, Texas, August 4-7, with the nomination taking place on Saturday, August 6.
The nomination will be decided by delegates from Green state parties and caucuses, according to this process http://gpus.org/convention-rules/#05
Individual state parties chose delegates via a variety of processes, including primaries, caucuses and state conventions. That process is described in greater deal here: http://gpus.org/committees/presidential-campaign-support/. The entire process for seeking the GPUS nomination is explained here http://gpus.org/committees/presidential-campaign-support/how-seek-green-presidential-nomination-2016/.
The process includes a formal recognition process where candidates must demonstrate a given level of grassroots support within the Green Party and a level of legal and financial organization. At present two candidates have received GPUS recognition - William Kreml and Jill Stein. A list of all candidates who have filed their campaign committees with the Federal Elections Commission or who otherwise will appear on a state party ballot, convention or caucus, is found here: gpus.org/committees/presidential-campaign-support/2016-candidates-seeking-gpus-nomination/
As the campaign develops, the GPUS Presidential Campaign Support Committee will print updates on which candidates are considered by which state parties and which receive delegates.
Additionally, news reports about all candidates seeking the GPUS nomination can be found here. http://www.gp.org/2016
Previous Green Party nominees have been:
2012 2008 2004 2000 and 1996
Jill Stein Cynthia McKinney David Cobb Ralph Nader
Cheri Honkala Rosa Clemente Pat LaMarche Winona LaDuke