Christ says there were 2 methods of conscription in the Classical period. During the Peloponnesian War, generals selected names to post on the 10 conscription lists which were known as katalogoi (whence, catalog). The 10 lists corresponded with the 10 tribes.
In the Archaic period, before the ten tribe reforms of Cleisthenes (508/507) hoplite service was mandatory for those who could afford the weaponry and armor. It may have been under Cleisthenes that the katalogos method of conscription was developed. Conscription was part of the process initiated when the Assembly approved a military action. The Assembly gave the number of hoplites needed and voted on which of the 10 generals should be in command. In addition to conscription, volunteers were welcome.
There were 4 stages in the conscription process:
- making up the list
- notifying the men by posting the catalogs in the Agora, on the base of the statues of the eponymous heroes of each tribe
- allowing for exemptions for reasons like being of the wrong age group (the right age was between 18-50 or 59) or without adequate wealth, although in the fourth century the state started supplying shield and spear, and
- assembling the men.
See "Conscription of Hoplites in Classical Athens," by Matthew R. Christ. The Classical Quarterly, Vol. 51, No. 2. (2001), pp. 398-422.