Please be aware that SketchUp does not implement true curves. It always approximates curves with sequences of straight edges. You can make a curve look smoother by increasing the number of segments, but at some point this will just increase the size of your model without making any difference in how it looks.
Also be aware that SketchUp does not support true solids. It is a “skin” modeler in which “solids” have no interior content, just a surface.
That said, there are several ways you can draw curves in SketchUp.
One is to use the various versions of the arc tool.
These all produce approximations of circular arcs. You can produce many shapes by stringing together circular arc sections. The tools have helpful inferences to facilitate connecting arcs smoothly.
Another is to get one of the Bezier spline tool plugins (search the Extension Warehouse or the SketchUcation plugin store - there are several available). These allow you to create and edit more complex curves.
A third is to use the free-hand tool, though it can be difficult to produce a nice curve that way unless you have a very steady hand.