If you are after traditional dances, try contacting the "Lykeio Ellinidon" (Lycaeum of Greek Women), which has branches everywhere and organises dances, mostly for exhibitions, but also for participation of the public. Their Athens phone number is +30-2103628978 (address is Dimokritou14, Athens 10673).

There are generally very few dance-specific events organised for general participation in greecem because there is no need for them. With dancing being inherent in ordinary Greek culture, most participatory opportunities are as part of some social event or celebration: wedding, christening etc. All you need to do is identify where one such celebration will be taking place near wherever you are (likeliest Friday-to-Sunday but could also be midweek), and then insinuate yourself into it, or rather approach the celebrants politely and ask if it would be OK to join in. Three times out of four they will have no problem with that, and even encourage you.