Do you mean you want to scale a shape layer that is a path or do you mean that you want to move the points on a shape layer path?
Shape layers have Transform: Shape tools that you can find by spinning down the > icons on a shape layer. You can manipulate the anchor point and move it to one side so that the Shape Layer/Contents/Shape 1/Transform: Shape 1/Scale property scales along one side.
If you want to Transform the points on a path the first thing you do is select the path. You can reveal it very easily by typing path in the Timeline Search field or by simply pressing 'uu' on the keyboard. Then press Ctrl/Cmnd + T to open up the Free Transform tool. Now you can grab any edge and pull it horizontally or vertically without changing the other edges. If you hold down the Ctrl/Cmnd key while dragging the Transform tool will change proportionately. Hold down the Shift key and Ctrl/Cmnd and you can constrain the proportions. When you are finished Escape or Enter will end the Transform.
With the path selected and the selection tool active (v) you can also drag a selection around one or more of the path points and then just drag them to where they need to be. You just have to pay attention to the cursor. When it changes from a black arrow to a white arrowhead (no tail) you can drag a selection around one or more points. If it is a black arrowhead you can select points or line segments and drag them around. If the cursor changed back to a black arrow then you need to select the Path in the timeline again to edit efficiently edit the path.