The tradition known as handfasting was celebrated in many cultures and in many different ages. There are several versions of this tradition today. I would recommend any couple considering a handfasting ceremony (either as part of a wedding, vow-renewal, or on its own) to research your own heritage to find out what was included and what the tradition meant for them.
My own knowledge is based upon Celtic reconstructionists, Druidry and paganism. The short history below is one of the Celtic theories. Unfortunately, so much of that time and the old beliefs were destroyed and lost to us. Handfasting can mean many things and it is a beautiful ritual. It was often the only way a couple be "officially" together if they did not subscribe to the official religion of their country at the time.
Historically, a handfasting was not a wedding or a legal contract between two people. In fact, it was more of a trial period than anything. There were times when certain faiths and beliefs were outlawed, so entire villages of people were forced into hiding. This was especially true during the historical period where anyone not practicing Christianity was accused of being a witch. It was there, hiddin in the forest, that handfasting became a ritual where two people promised to be true to one another, to live as partners for a defined period. Usually this translated into one year. At the end of that year the couple would decided whether to make it final or go their separate ways.
As years passed, the tradition became something akin to an engagement. Today, handfasting is often used as a part of a formal wedding ceremony, a commitment ceremony or at an engagement party.
One particular tradition (Welsh) would have the woman remove a ribbon from her hair and that ribbon would be used to "fasten" the hands of the couple together. The officiant would bless the ribbon and the couple.
Today, many couples choose cords or ribbons based on color. Each color represents a different virtue that they would like to invite into their new marriage. There is a great chart to look over here that will help you decide.
A great way to include children or family and friends is to ask them before your handfasting to hold one of the cords or ribbons. As the ceremony happens, we can invite them up one at a time and have them bind your hands together. Its just a beautiful and meaningful way to have several people become a true part of your lives together.