There are probably many different ways to achieve it. I used Extra Objects and F2 add ons.
Start with adding a Spiral (Add-->Curve-->Spirals). Play with its settings in a Tool Shelf (T)
Convert your curve to the mesh (press Alt+C-->Mesh from Curve). Then select the whole mesh (A) and extrude it (E) as pictured below.
Being in Edit Mode add a Circle with the equal number as the Spiral's steps number. Extrude the Circle and use the snapping tool to snap its edge loop to the bottom vertex of a curved mesh. Now use the knife tool (press K,LMB, next C for a straight cut and then Z to cut through) as pictured below. Delete vertices above and below added cuts.
Fill the gaps with F (enable the F2 add on). You may also use the bridge tool to do it.
If you want to sharpen edges with edge loops (Ctrl+R) retopologize the top part as pictured below. This kind of geometry'll also smooth the end of the curvature.
Here's my final topology (with no tris and n-gons), that allows me to crease the edges.
Use proportional editing with a Sharp falloff type to adjust volute's proportions as you like.