It’s published by Newsquest (Wiltshire), who also publish the paid-for weekly tabloid the Swindon Advertiser from the same editorial offices in Swindon. (The Star doesn’t have a web presence of its own; the link below is to the Advertiser‘s website.)
Its origins go back to the foundation of the Wiltshire Star and Cirencester Advertiser in 1969, but it didn’t appear under its present title until 1988.
It comes out on Thursdays. An e-edition’s also available free on the website – registration is encouraged but not necessary.