Slide Keys

Track View > Highlight keys in the Key window. > Track View toolbar > Slide Keys

Use Slide Keys to move a group of keys (highlighted keys plus all the keys to one end of the animation). The direction that you drag determines which group of keys moves:

Dragging to the right moves the highlighted keys, plus all keys to the last key of the animation, forward in time.
Dragging to the left moves the highlighted keys, plus all keys to the first key of the animation, backward in time.

Slide Keys is a way to split the animation at the highlighted keys and spread the ends apart. Slide Keys is available in Edit Keys mode.

You can clone keys and insert them elsewhere in your animation curve while offsetting existing keys by the length of time occupied by the cloned keys by dragging while holding down Shift. Based on the length of your selection, the existing keys to the right of the selection move forward in time (that is, to the right) to allow the new key insertion, whether you drag to the right or the left.

Procedure

To slide a selection of keys:

Click Slide Keys on the Track View toolbar.
Highlight one or more keys.
Drag to slide the keys to the right.

The keys following your selection move to account for the offset produced by sliding the keys.
Highlight another group of keys.
Hold Shift while dragging to slide the keys to the right.

The keys following your selection move to the right by the length of time occupied by the cloned keys.