The preview shows Oscar winner Zellweger playing the troubled entertainer as she performs on stage, cares for her children, pops pills and deals with financial problems.
"I don't have a home. I can't even get a manager," she complains before heading to England for what she hopes will be a series of career-reviving shows in 1968.
A synopsis for the film explained: "It is 30 years since she shot to global stardom in The Wizard of Oz, but if her voice has weakened, its dramatic intensity has only grown. As she prepares for the show, battles with management, charms musicians and reminisces with friends and adoring fans, her wit and warmth shine through."
Garland died from a drug overdose in London in 1969. She was 47.