There are times when one will see many people getting up from their tables and joining in the dance with others, and one can take one's cue from this that it is appropriate to do so yourself. On the other hand, if you see someone (usually a man) get up from his table and lead a dance of his parea (those who had been seated with him), often first going over to speak to the musicians and throwing some paper money at their feet, all this should be taken to mean that someone has paid the band to play his favorite tune for him to lead the dance for his personal party, and that by no means should you get up and join in. Chances are, if you did so, the parea would not throw you off the dance floor (knowing that you were just an outsider ignorant of the customs), but most likely you would feel quite foolish, especially the people next to you started doing fancy steps and you couldn't follow, with many eyes fixed in amusement on your inadvertent blooper. It is also important to take note of the fact (assuming that you are not a veteran folk dancer) that in line dances (as opposed to couple dances), the line of dancers, for all that it appears to be a circle, is really a broken circle with a leader, who is moving the line to the right. So if you get into line, don't go to the far right end of the line and take the leader's hand, or you will be seen to be usurping the leader's role and be expected to lead all the dancers with your own fancy variations of the steps.
This is a free form dance that is done these days mostly to bouzouki music (whether of the old classic type, or of the more modern flashy, plate smashing or bottle smashing travesty of the older form). It is basically a highly improvised solo dance, though sometimes two men will get up and dance it separately, but within the same area. Despite the fact that it is improvised, it is not free form dancing like modern, jazz, or rock 'n roll dancing. The way of moving-- the type of steps executed-in this dance, though individualized, belong to a definite tradition, and can easily be wrecked by someone unacquainted with the tradition getting up and rocking out . Though it is harder to wreck a line dance, given the larger number of dancers who know the steps and the feeling of the dance, even then , foreign participants should make an effort to try to follow the simple step pattern done by those on either side of oneself, rather than doing one's own thing. Line dances (and couple dances too) are a form of communiction (and communing ) among Greeks (as is all folk dancing everywhere), and if you want to participate, do so with sensitivity to what is going on. This is not to discourage people moved by the music and dance from joining in, but merely to urge tuning into what is happening rather than 'doing your own thing' (and hence standing out like the old 'sore thumb'.