If you are going to or coming from another Tuscan town, see Tuscany#Get_around for more info on bus service.
Local and interurban buses all seem to stop by the railway station Chiusi C.T.. You can buy bus tickets at the newsstand within the railway station. The bus stops are to the left of the station doors facing town. The orange local buses stop near those doors while the blue interurban buses are further to to left. Keep in mind that a blue interurban bus might serve your local stop as well as an orange local bus. The bus stops serve both directions of travel, so check the destination sign or confirm with the driver.
The website for Siena Mobilità (http://sienamobilita.it/o...) has bus schedules orari for local routes in Chiusi. Click the tab Servizio urbano Chiusi. Also check the tab Servizio extraurbano as there are several interurban routes that also serve Chiusi.