You can think of the paint brush as a cylinder projected along the surface normal of the mesh geometry, centered at the point on the mesh under your cursor.
The circular brush outline shows you the radius of the brush. The inner circle shows the brush's falloff (or inner radius.) You probably figured this out already, but the small line sticking out from center of the brush is the mesh surface normal.
To paint, hold down the Left Mouse Button and drag over the mesh's surface. You can also hold down the Shift key while painting to erase instead.
Mesh painting also works in the VR Editor. For the controls for Mesh Paint in VR, see the VR Mode Controls.
Paint will be applied to the surface each time you click, and also each time the mouse position changes by dragging. Also, if Brush Flow is enabled, paint will be applied every time the scene is rendered.
You can only paint in perspective viewport windows.