For detailed information and images on how-to, check http://szepark.hu/english/index.htm
General outline:
1. buy parking ticket in designated shops/kiosks, for different tickets and system plz check above links
2. find parking place, park
3. validate your ticket
or only for Hungarian T-Mobile mobile phone subscribers:
see http://szepark.hu/index.htm for sending sms as a way of buying your ticket.
Make sure you park with ticket, the fines start with 7.000 HUF and triple after 8 calendar days...