The Çoçek, is a very simple Roma dance usually performed in a line to a 4/4 beat. It doesn't involve tambourines, flying petticoats, stamping or high kicks with the legs. It is reasonably sedate.
Start with feet together and arms at shoulder height. You'll be holding hands with your 'neighbours'
1) Right foot takes one step to the right 2) Left foot steps behind the right foot 3) Right foot steps out to the right again 4) Left foot comes to rest at the side of the right foot (start position) 5) Right foot takes one step forward, left foot follows and repeats side step pattern but to the left. 6) The left foot steps back and the right follows ready to start the 'square' again.
There are many versions of this dance, some travelling right to left, some with little hops and weight changes but this is the basic one on which to perhaps build your own routine.
Thank you Saviya for this description. But this is only one of the possibilities for dancing the cocek. I have been lucky to learn it with the great Simona Jovic ( it is a famous european romani dance teacher, I posted a word about her here : lotusflower.proboards3.com/index.cgi?board=rom&action=display&n=1&thread=87). She is serbian and she's been dancing the cocek since ever! It can be danced by both women and men (just as you described) but also by women only. In that case it is very oriental, influenced by the turkish dances. It is danced especially in Southern Serbia, Macedonia and Bulgaria.