If on a selected curve you press the left button of the mouse in a control point, the square will become red., you have selected the control point. There are some actions you can do in this situation:
press key `d'. This delete the control point.
press key `a'. A new point control will be added in the cursor position.
press key `m'. You move the control point position. The new position will be the same of the cursor.
You can also click and drag on a control point to move it.
You can use the grid ( Option|General... ) to limit the positions of the point.