Hold down + (Windows) or + (Mac), click the curve and drag along the curve.
When you are sketching, you can snap a brush to a curve (or surface isoparametric curve or curve-on-surface). This allows you to use curves as sketching guidelines.
The brush profile will jump onto the curve.
To set the brush curve snap tolerance, choose Preferences > General Preferences, then choose Paint from the left side of the option window, and set Brush Curve Snap Tolerance to the number of pixels the brush cursor must be from a curve in order for the brush profile to jump onto the curve.
You can snap to invisible curves (see ObjectDisplay > Invisible) or curves on invisible layers (Layers > Visibility > Invisible).