how do I get the drawing, in vetor format, I made in draw app to my desktop using creative cloud and a .ai format to open on the draw app?
To send your Draw work to Illustrator CC... from an open canvas, tap the Share icon (square with an arrow) in the upper nav. As long as your signed in to both the mobile app and the desktop with the same Adobe ID, your Draw work should automatically open in a new artboard on the Illustrator desktop.
Right now, it's not possible to bring a .ai file into Draw as an editable file. That work can only be brought into the app as an image.
Hope that helps.
If you don’t have the CC version how do you then?
I have CS5.1.
Adobe Draw is not compatible with the apps in CS5.