Example sentences from the web:

• My cousin turned up out of the blue on Christmas Day.
• My sister Mary appeared on my doorstep out of the blue, after years with no word from her.
• You turn up out of the blue, begging for my help in something completely illegal!
• Stephanie called me out of the blue yesterday morning.
• He just broke up with me out of the blue, and I have no idea why. 

Words you may not know:

TO TURN UP (past simple: “turned up”)=> to appear or come to light unexpectedly or after being lost.
TO BEG (gerund: begging) => to ask someone to give or do something; to implore.