Sukkot is immediately followed by Shemini Atzeret and Simchat Torah.

In Israel  Shemini Atzeret and Simchat Torah are celebrated on the same day.

Outside of Israel  Simcḥat Torah is celebrated the day after Shemini Atzeret.

Simchat Torah marks the conclusion of annual Torah Reading and the beginning of a new cycle. This accomplishment is celebrated by taking the Torah scrolls out of the ark, and circling the synagogue with them while dancing and singling.

The circling of the synagogue with the Torah is called Hakafot   הקפות

When is Simchact Torah and Shemini Atzeret celebrated, in 2012?

In Israel:

Shemini Atzeret and Simchat Torah are celebrated from October 7, 2012 sunset until the first stars on Oct 8, 2012

Outside of Israel:

Shemini Atzeret is celebrated from October 7, 2012 sunset until the first stars on Oct 8, 2012

Simchat Torah  is celebrated from first stars of October 8, 2012  until the first stars on Oct 9, 2012