This 11 minute movie produced by Michele Gingras, illustrates all the steps to achieve circular breathing on the clarinet.
Circular breathing is a technique used for different purposes throughout musical times. Middle Eastern double reed players produce a drone with continuous and uninterrupted airflow, and Scottish bagpipers use an air sack to store air to create a continuous sound.
Technically, circular breathing is the production of a continuous sound by using the cheeks as an air reservoir and breathing through the nose while the stored air is forced from the mouth into the instrument. In traditional repertoire, it is almost always possible to find a place to breathe, although some long virtuoso passages could be played with this technique. Circular breathing also produces spectacular effects in contemporary music.
Follow the instructions on this video, and you should be able to play this technique within a week or two.
Please note that Prof. Gingras uses the word "expulse" instead of "expel" in the video (too much French this summer!). This will be corrected in a future video.
Good luck!