By default in the Graph Editor, you can simply click and drag to move a selected key on a curve.

To move keys on a curve

1. Select the animated object whose curves you want to edit.
2. In the Graph Editor, select a key in the graph view area, then drag to move it.

   Moving the key changes the shape of your curve.

If you prefer to disable this single-click editing workflow, you can disable the Left Mouse Button Alters Selections preference (Window > Settings/Preferences > Preferences) and use the Move Nearest Picked Key Tool to explicitly move keys with the middle mouse button. (Disable Left Mouse Button Alters Selections in the under the Graph Editor heading in your Animation preferences.)

To move keys along an animation curve using the Move Nearest Picked Key tool

1. In the Graph Editor, select the curve.
2. Select the key you want to move.
3. Select the Move Nearest Picked Key tool from the toolbar.

   See Select Keyframe Tool.

4. Middle-drag the key along the curve.