The Attic tablets are the earliest large body of curse texts anywhere, running from the fifth century BCE, and they are the closest thing the subject has to a starting point. They were recovered over more than a century from graves, wells and sanctuary deposits in and around Athens, and Richard Wunsch edited them in 1897 as a supplement to the third volume of Inscriptiones Graecae. The DTA numbers still used to cite them are his.
The earliest examples are startlingly bare. Many consist of names and nothing else, inscribed on a lead sheet which is then folded, sometimes pierced with a nail, and put where it cannot be retrieved. There is no address to a god, no reason given and no request. Writing the name and putting it out of circulation appears to have been the whole of the act.
Over the following centuries the texts grow. Deities are addressed, most often the powers of the underworld. Reasons appear. Formulae develop, and by the Roman period the same phrases can be found across the Mediterranean. Watching that sequence is the reason the Attic material is disproportionately important: it shows an elaborate late antique technology assembling itself out of something extremely simple, rather than arriving fully formed.