For the basics on the festival of Simchat Torah, Tablet has a nice run-down. But here are some other facts you might not know, from Avraham Ya'ari's classic history of the festival, 'Toldot Chag Simchat Torah' ('The Origins of the Festival of Simchat Torah,' pub. in Hebrew by Mossad Harav Kook).
Whilst we often pride ourselves on / lament (depending on who you are...) the unchanging nature of our tradition, this history shows how enormously fluid some of our traditions actually are. Among the fascinating points:
-- Simchat Torah originated in Babylon and was not celebrated in Israel until the end of the first millenium - ie it is a total diaspora festival. The reason is that in Babylon, the Jews had the same one-year cycle for reading the Torah as we do today, whereas in Israel they finished the Torah every three / three-and-a-half years, and not always on the same date. When the communities in the land of Israel finished the Torah, they would hold a festive meal, but no 'Simchat Torah' as we know it.
-- The festival originally did not involve reading from Genesis, but merely finishing Deuteronomy. Hence, the original term was not 'chatan Torah' (Bridegroom of the Torah/Law) but 'chatam Torah' -- sealer of the Torah. There was, of course, no chatan Bereshit.
-- The original name wasn't 'Simchat Torah' but 'Yom Habrachah' -- the day of the blessing, named after Vezot Habrachah -- the last chapter of the bible which was read on that day, and also after the haftarah they read then, in which King Solomon gave blessings (I Kings 8:22). In Spain it was known simply as 'the last Yom Tov of Chag.' In North Africa it was 'Yom Hasiyum' -- the day of completion. The name Simchat Torah originated in Spain, after the first millenium.
-- Hakafot on Simchat Torah were not known at all until the last third of the 16th century, and the first time we hear about it is in Tzfat in the days of the Ari, from where it spread out to other communities. Previously, some communities in Ashkenaz took out all the Torah scrolls, but it took 150 years for the custom of hakafot to spread, after it was mentioned in several books and after Jews from the land of Israel travelling to other communities helped institute it.
-- There are a few customs for Simchat Torah which we know about because there are rabbinic responsa addressing whether they were permissable. These include bringing spices and incense to shul and burning them in front of the Sefer Torah. In Israel between the 17th-19th centuries, during hakafot, people used to hold lit wax candles, and this custom also spread (in several places they used to use havadalah candles...). Another fire-related minhag was getting the children to burn the schach from succot on ST.
-- Other lost minhagim: Worms - they would dance around bonfires on Simchat Torah. In other places in Ashkenaz celebrations of Simchat Torah involved jumping over a fire. In a small number of communities the singing on Simchat Torah was accompanied by musical instruments played by non-Jews - and at times by Jews (In Venice, for example, there was a debate over whether the players could use an organ as it was used in churches; other instruments, however, were ok). In other places eg. Sarajevo, they played drums during hakafot. In some Ashkenazi communities, particularly in Poland and the Balkans, in the seventeenth century, they let off fireworks and firecrackers. Many people used to eat and drink in shul whilst the Torah was being read, often food baked by the women of the community...
-- There were many special customs for the women on Simchat Torah, including in some places, decorating the Torah scrolls after Minchah on Shmini Atzeret in preparation for Simchat Torah; selling the 'women's mitzvot' for the rest of the year - which included, I note, sweeping the floor of the shul -- throwing candy on the chatanei Torah; and honouring the wives of the chatanei Torah as 'Kallot Torah.' Once hakafot began, women were graciously allowed to watch proceedings, even in communities such as Yemen where women generally did not come to shul at all. In Southern Russia, women were actually allowed into the men's section; in Lithuania, women and girls came into the synagogue to kiss the Sifrei Torah; in Baghdad, each shul used to lay out all of its sifrei Torah and both the men and the women used to go from shul to shul kissing each scroll.
-- The tendency to confuse Simchat Torah with Purim has a long history. The priestly blessing was changed from Mussaf to Shacharit so that the Cohanim would not be drunk when they said it; in some communities it was cancelled altogether. There are also a number of poems about Simchat Torah which equate the festival with drinking and frivolity from very early on, as well as rabbinic warnings on the matter. There were lots of parodies of religious songs (including Echad Mi Yodeah, and Kiddush) that were popular on Simchat Torah, and there was also a customof appointing a 'Purim rabbi / Purim head-of-kehillah' on ST and of allowing the young men to take over proceedings, including the old shtick of tying people's tallitot together, stealing food from ovens, etc. etc. etc. This was all very widespread but apparently Salonika was particularly known for letting the service become jokey.
Chag sameach everyone!