We generally do this dance in a circle, facing in, with everyone singing and clapping. One by one we jump into the center and act out the verse.
You could also do it with the lord (or lady) of the dance leading the singing in the middle, with the dancers circling and miming around.
Likewise, although when we do it everyone usually sings the whole thing together, you could do it as a call-and-response:
One: There was a pig went out to dig
All: Candlemas Day, Candlemas Day
One: There was a pig went out to dig
All: Candlemas Day in the morning.