Alternately, hold down the ALT key when selecting the feature(s) to move to automatically enter move mode for the selected feature(s)/vertices. Once finished, simply hold down the left mouse button and drag the features to the desired new location.
To move only the selected features(s) either horizontally or vertically, hold down either the 'X' or 'Y' keys on the keyboard to restrict the movement to that axis. Holding down both keys will move the feature(s) diagonally.
To undo a feature move, select the feature(s) to move back and then select the Restore Original Shape of the Selected Feature from the right-click sub-menu Move/Reshape Feature(s). Selecting this options reverts the selected feature to the original, or last saved, shape before editing began.