It was pretty widely celebrated in Scotland as one of the main holidays of the season (given that at this time, Christmas wasn't celebrated) and the celebrations haven't really changed that much. They vary across the country but some of the common ones are

There is a poem from 1805 by J. Nicols that says "Ere new years' morn begin to peep At doors, the lasses sentrie keep, To let the first-fit in" which is a tradition that the first person that turns up at yours after midnight brings luck (and various other things such as whisky).

Then there are a lot of traditions involving fire which likely date pretty far back but due to lack of documentation it's hard to know how long some of them have been celebrated.

The word Hogmanay also goes back pretty far and there is a reference from 1790 that says "In..Scotland, and in the North of England, till very lately, it was customary for every body to make and receive presents amongst their friends on the eve of the new year, which present was called an Hagmenay."

I can't really say much else here because I don't have sources for the rest and because a lot of it is just tradition with no evidence for how old it is but if you want to learn a bit more there are plenty of sites that tell you about the various traditions of Hogmanay - also since a lot of places have local customs it makes it even harder to figure out dates.