In sequence dances, everyone should be using the same fixed pattern of steps. In solo or group line dances, all generally face the same way in whatever rows and columns fit the room. In folk, country or barn dances, groups of dancers form a set and these sets are arranged to fit the room. Otherwise (ie for most paired dances), the line of dance runs anticlockwise around the edge of a room and couples spread out along it.
The man usually starts on the inside of the circle and the lady on the outside. They may be facing each other or both facing the LOD. In modern dances, the man always begins with his left foot. Therefore the lady begins with her right foot, except when shadowing or solo. In older folk dances the man begins with his right foot.
Some couple/pair dances can be progressive. During the sequence, at a particular point, all the partners will separate. Then (usually) each man will progress along the LOD while each lady moves against it to join up with the next partner in line before continuing the sequence.
Step instructions given here are my interpretation of what I've seen. They may not match the original creator's description. Unfortunately, for many sequences I have no idea who the creator was. I will correct any mistakes in the steps when I find an accurate source for each dance.
¹ = solo/line dance
² = couple dance
³ = group dance