Googling ostracism Athens led me to this site, http://www.csun.edu/~hcfll004/ostracis.html . The second quotation (headed Philochorus) explains that first they voted on whether to have an ostracism or not, and then on who to ostracise. You had to get a minimum of 6000 votes to be ostracised and then you had 10 days to leave Athens, though you could still receive the income from your property there. The site also has a picture of an ostrakon.

Bingley

Bingley