Tartan was originally the term used for the way the cloth was woven. It actually had nothing to do with a plaid pattern at all. (Incidentally, plaid originally meant "blanket" and had nothing to do with a design or pattern).
The oldest piece of tartan dates to the 3rd century AD. Found near Falkirk, in an earthenware pot, it was covering about 1,900 silver Roman coins. It had a checked pattern of undyed wool which consisted of dark brown and light brownish green, two common colours of the native Soay Sheep.
It wasn't until the 16th century that we have a record of tartan similar to the way we know it today. By that time, it had become the dress of the common man in the Scottish Highlands. However, there is no known clan affiliation with any design or pattern. It appears as if a person would wear what they liked or had available. At this point, clan affiliations were shown in other ways, such as putting a ribbon or feather of a particular colour in your cap.
By the mid-1600s district patterns started to crop up, although this may have occurred because it was easier for the local weaver to make one large length of cloth rather than several smaller ones. This would leave a person little problem as to "what to wear today".
One item of note here is that most areas were populated by a family or a few families. So the district tartans were, in that respect, clan tartans by default. Another item of note is that, if you are going to wear a tartan for re-enactment purposes you do not have to worry about your family lineage or offending someone for wearing a pattern that is not "yours". You may want to look into the district patterns, especially if you are portraying a later time period; however, it is most likely not a necessity.
After the Jacobites (Scots loyal to the Scottish crown that was usurped in 1688) rebelled at the Battle of Culloden in 1746, the English banned the wearing of all tartan. This ban was repealed in 1782 and the Scots had a widespread hope to re-establish the identity of Scotsmen as Scotsmen (and not English or British). They were helped out by Sir Walter Scot in the early 1820s, as well as King George IV, who threw great parties where no one was admitted unless in "true highland dress". Each clan chief was expected to identify and validate a pattern for their clan. With this, the concept of the "clan" tartan was strongly set in place. Queen Victoria, who had a great liking for all things Scottish, only encouraged it all. The tartan, therefore, proceeded to become the National Dress of Scotland.
Today there are over 2500 registered tartan patterns as well as hundreds of non-registered and private variations, encompassing Scotland, Ireland, Canada, the US and even Australia.