By default, the Move Nearest Picked Key Tool lets you single-click and drag to adjust tangent handles and keys on a selected curve. You can also set the tool to enable single-click editing for all curves (regardless of whether they are selected).
To allow single-click manipulation for all curves
When Selected only is on, single-click editing works on selected curves. When off, you can single-click to edit all curves.
If you want to use a single-click tangent editing workflow, set tangent handles to always display by selecting View > Tangents > Always from the Graph Editor menu bar.
To allow single-click manipulation for selected keys on a curve
When this preference is enabled, you can move a selected key with a single click and drag.