Take a look at these tutorials for using nonlinear animation, which typically refers to the process of modifying and combining existing animations in order to produce a new motion, from Autodesk.
This is done by converting lower level animation (keyframes and anim curves) to a higher level, clip representation of the same animation. Once in clip form, a number of operations can be applied in order to augment the underlying animation including: moving, scaling, sequencing, reordering, re-timing, blending and layering.
The primary tool for working with nonlinear animation in Maya is the Time Editor. The Time Editor is a powerful and versatile UI with accompanying toolset. In this series of demonstrations I cover a range of related nonlinear animation workflows.
Nonlinear Animation Workflows with the Maya Time Editor