Use it to express doubt about the truth or reliability of a statement someone has made. They claim it's the deal of the century, don't you believe it!
Pro Tip 2/3
Informal Tone
It's a casual phrase, best used among friends or in informal situations, not formal ones. The brochure says 'fun for all ages', don't you believe it!
Pro Tip 3/3
Surprising Reveal
It can hint that you know something others don't, often used before revealing the truth. Looks like just an old barn, don't you believe it! Inside is a dance hall.