The Curve tool is trickier to use than the Line tool. It can be difficult to learn how to use, and it is difficult to explain. Your best bet is to experiment with it, but be patient, because it will take a lot of getting used to before you get very good at making curved lines that are the shape that you want.
Like the straight Line tool, the Curve tool can make lines in various thicknesses and colors.
Try experimenting with various techniques for making lines. Try clicking and dragging to make one kind of line, or clicking and releasing two endpoints. Click a third point to determine the curve. Try dragging an already drawn, but still active, multi-point line to distort its curve.
The Curve tool can be very frustrating, especially for beginners, especially since the Undo command can only be used to undo the last change you've made to your image. Just keep practicing!
I made these curved lines using the curve tool. The green line has two bends in it (the maximum). The red line just has one curve. Just draw a line like you would with the straight line tool, then click and drag to bend the line and make it curve. The grey loop was created by employing a single click to start a point, then dragging the curved line open to create a full loop.