This is one of my favorite holidays and one I could have been apart of it's celebration but unfortunately was not.
I am going to concentrate on the Swedish traditions since that is where half of my family comes from though the holiday is celebrated in many other countries.
First a little history to give context to where the celebration comes from. St Lucy or St Lucia depending on how you want to spell it is a martyr in the Christian faith and one of the only ones venerated by the protestant Scandinavian countries. There are at least two stories about her one where she would not burn and another were she needed both her hands so she made a wreath for her head and put candles in it so she could see. In both stories she is a young women or girl.
Tradition in Sweden now has it that the eldest daughter will wear a white robe with a red sash and wreath of candles in her hair and her younger sister would wear the same robe and sash but carry one candle. They will sing a traditional St. Lucy song while bringing their mother and father coffee and a special St. Lucia Bun (Lussekatt)
Though out the country now towns will appoint a St. Lucia to represent the whole population and there will be a procession in the street. Boys will even get involved dressing in several different outfits; ginger bread men, carrying lanterns, tomtenissar or stjärngossar (Star Boys, they dress in similar outfits but have a pointed hat instead). Schools will also elect a St. Lucia and her retainers and these will visit nursing homes and hand out sweets another thing they are known for.
Interestingly there has been some controversy in the past few years where males have been elected to be St. Lucia but many have opposed them being allowed to serve in the role.
I am not sure why my family never celebrated this even though we lived in Minnesota where I understand it is not unusual for it to be observed and my grandparents did recognize many traditional Swedish traditions, it may have been that they only had boys so had no one to pass this tradition on to but I feel it would have been a nice one to pass down.