In 2009 you had the use of the Axis tool to sketch the line of the desired axis of rotation. This has disappeared in 2010 onwards and is causing confusion (note this still exists for normal component families and in-place families).The answer is quite simple:
In this example I'm working in the Conceptual Mass template but this also applies to in-place mass elements as well.
Start by drawing a line or reference line (either option will work) to define the axis of rotation. Whats the difference? A line will disappear after the shape has been created. A reference line will remain in place. Also, if you move the reference plane afterwards, the shape will move with it (its associated). In this example we are using a reference line.
Draw the shape you wish to revolve.
Select both elements by holding down CTRL on the keyboard to multiple select.
If you have done it correctly, an icon should appear on the ribbon called 'Create Form'. Hit the drop down and choose 'Solid Form'.
The Revolve is created by default at 360 degrees rotation. The line or reference line used for the axis can be deleted if you no longer require it.
Select any part of the solid and from the element properties, change the rotation angle to something other than 360.
You can now select the profile of the revolve and move the orange grip by clicking and dragging.
Finally, try selecting the reference line and dragging one of the end grips to rotate axis. Notice the solid moves with it. This is useful for applying parametric behaviour to the reference line.