Measure your ring.  You'll need the width and the circumference.

Create a rectangle using these two measurements.  

Turn off output as this will only be used for organizing the design.

Fill your rectangle with your desired design.

I made two with butterflies and smiley faces but you can use anything.  I don't suggest using too complicated of a design as this is going to be very small and we want it to be clear.

Each ring may vary a little so don't forget to check the circumference each time.

Set the designs to Engrave.
 

Set your machine to rotary attachment.

Use the chuck setting and use the metal pieces for your chuck as those hold jewelry well.

Enter your perimeter (circumference).  Mine is 70mm.

I set power to 80 and speed to 400mm/s

Set your rotary so that the measurement lights are at the highest point of the ring

Refresh the camera on the Ultra

Use the picture to align your design with the green line.  

Make sure the rectangle has Output set to off.

You are ready to engrave.