The roots of Hogmanay perhaps reach back to the celebration of the winter solstice among the Norse, as well as incorporating customs from the Gaelic New Year's celebration of Samhain. In Rome, winter solstice evolved into the ancient celebration of Saturnalia, a great winter festival, where people celebrated completely free of restraint and inhibition. The Vikings celebrated Yule, which later contributed to the Twelve Days of Christmas, or the "Daft Days" as they were sometimes called in Scotland. The winter festival went underground with the Protestant Reformation and ensuing years, but re-emerged near the end of the 17th century.
There are many customs, both national and local, associated with Hogmanay. The most widespread national custom is the practice of 'first-footing' which starts immediately after midnight. This involves being the first person to cross the threshold of a friend or neighbour and often involves the giving of symbolic gifts such as salt (less common today), coal, shortbread, whisky, and black bun (a rich fruit cake) intended to bring different kinds of luck to the householder. Food and drink (as the gifts) are then given to the guests. This may go on throughout the early hours of the morning and well into the next day (although modern days see people visiting houses well into January). The first-foot is supposed to set the luck for the rest of the year. Traditionally, tall dark men are preferred as the first-foot.
Each area of Scotland often developed its own particular Hogmanay ritual.
An example of a local Hogmanay custom is the fireball swinging that takes place in Stonehaven, Aberdeenshire in north-east Scotland. This involves local people making up 'balls' of chicken wire filled with old news paper, dried sticks, old cotton rags, and other dry flammable material up to a diameter of 60 cm. Each ball has approximately 1 m of wire, chain or nonflammable rope attached. As the Old Town House bell sounds to mark the new year, the balls are set alight and the swingers set off up the High Street from the Mercat Cross to the Cannon and back, swinging their burning ball around their head as they go for as many times as they and their fireball last. At the end of the ceremony any fireballs that are still burning are cast into the harbour. (Here's a video)
Many people enjoy this display, which is more impressive in the dark than it would be during the day. As a result large crowds flock to the town to see it, with 12,000 attending the 2007/2008 event. In recent years, additional attractions have been added to entertain the crowds as they wait for midnight, such as fire poi, a pipe band, street drumming and a firework display after the last fireball is cast into the sea. The festivities are now streamed live over the Internet.
Another example of a pagan fire festival is the burning the clavie which takes place in the town of Burghead in Moray.
In the east coast fishing communities and Dundee, first-footers used to carry a decorated herring while in Falkland in Fife, local men would go in torchlight procession to the top of the Lomond Hills as midnight approached. Bakers in St Andrews would bake special cakes for their Hogmanay celebration (known as 'Cake Day') and distribute them to local children.
In Glasgow and the central areas of Scotland, the tradition is to hold Hogmanay parties involving singing, dancing, the eating of steak pie or stew, storytelling and consumption of copious amounts of alcohol, which usually extend into the daylight hours of January 1.
Institutions also had their own traditions. For example, amongst the Scottish regiments, the officers had to wait on the men at special dinners while at the bells, the Old Year is piped out of barrack gates. The sentry then challenges the new escort outside the gates: 'Who goes there?' The answer is 'The New Year, all's well.'
An old custom in the Highlands, which has survived to a small extent and seen some degree of revival, is to celebrate Hogmanay with the saining (Scots for 'protecting, blessing') of the household and livestock. This is done early on New Year's morning with copious, choking clouds of smoke from burning juniper branches, and by drinking and then sprinkling 'magic water' from 'a dead and living ford' around the house ('a dead and living ford' refers to a river ford which is routinely crossed by both the living and the dead). After the sprinkling of the water in every room, on the beds and all the inhabitants, the house is sealed up tight and the burning juniper carried through the house and byre.
The smoke is allowed to thoroughly fumigate the buildings until it causes sneezing and coughing among the inhabitants. Then all the doors and windows are flung open to let in the cold, fresh air of the new year. The woman of the house then administers 'a restorative' from the whisky bottle, and the household sits down to their New Year breakfast.
The above info is from Wikipedia, and from the Encyclopaedia of Superstitions, Folklore, and the Occult Sciences of the World 3 Vols. we have this small tidbit on Hogmanay:
The last day of the year is called in Scotland, Hogmanay. On this day the children in small towns perambulate among the neighbors of the better class, crying at their doors, "Hogmanay!" or sometimes the following rhyme:
Gie's of your white bread
and none of your gray!
In obedience to which call, they are served each with an oaten cake.