While you were riding did you lose all power at once or slowly?
Does it sound like it wants to turn over or does it do nothing when trying to start?
Check the battery it may need replacing check to see how strong it is.
Check to see if you have a spark.
Make sure that you have compression. Anything over 110 PSI is good 130-150 PSI better. Under that you may have lost the piston or rings.
http://www.49ccscoot.com/manuals/manuals.html ZX 50 manual on this page look at Page 2-16 for trouble shooting help