The basic approach to the region adaption function is to first define a region:
The hexahedron (quadrilateral) is defined by entering the coordinates of two points defining the diagonal.
The sphere (circle) is defined by entering the coordinates of the center of the sphere and its radius.
To define a cylinder, specify the coordinates of the points defining the cylinder axis, and the radius. In 3D this will define a cylinder. In 2D, you will have an arbitrarily oriented rectangle with length equal to the cylinder axis length and width equal to the radius.
A rectangle defined using the cylinder option differs from one defined with the quadrilateral option in that the former can be arbitrarily oriented in the domain while the latter must be aligned with the coordinate axes.
You can either enter the exact coordinates into the appropriate real entry fields or select the locations with the mouse on displays of the grid or solution field. After the region is defined, each cell that has a centroid inside/outside the specified region is marked for refinement.