How are gravitational waves exactly produced? I was thinking about gravitational waves, and I found out that I may have a doubt about their production.
Assuming the whole calculations find a wave-like solution to be understood, I was wondering about the real reason/way by which gravitational waves are produced: I have always been taught that a wave is produced by a perturbation created by the motion of an object.
Gravitational waves arises when huge massive bodies do perturb the space-time itself but here it's the unclear fact: it's the motion of masses itself that perturb the space-time? Because I'm having some hard times in understanding if gravitational waves are/are not produced simply by a moving massive body..
Because in this way, "we too" may produce gravitational waves (whose frequency would be extremely small).
 A: Gravitational waves are generated in a manner analogous to electromagnetic waves. 
Classically, changing electric or magnetic fields can generate electromagnetic waves, a radio antenna being a good example, and also radiation is emitted by accelerating or decelerating particles. Maxwell's equations are "simple" enough as one is dealing with vector fields. This is reflected in the quantum mechanical carrier of the electromagnetic field, the photon, which has spin one.
In General Relativity the mathematics is more complex, still, gravitational waves are expected for "changing gravitational fields" , in quotes, because the gravitational field emerges from the space curvature posited by GR.  Since  one is dealing with tensor fields , the quantum mechanical carrier (in the effective quantizations of gravity used up to now) is the graviton of spin two. 

gravitational waves transport energy as gravitational radiation. The existence of gravitational waves is a possible consequence of the Lorentz invariance of general relativity since it brings the concept of a limiting speed of propagation of the physical interactions with it. By contrast, gravitational waves cannot exist in the Newtonian theory of gravitation, which postulates that physical interactions propagate at infinite speed.

This illustrates the space distortions as the wave passes:

The effect of a plus-polarized gravitational wave on a ring of particles.


So, as with electromagnetic waves,

In general terms, gravitational waves are radiated by objects whose motion involves acceleration, provided that the motion is not perfectly spherically symmetric (like an expanding or contracting sphere) or cylindrically symmetric (like a spinning disk or sphere). A simple example of this principle is a spinning dumbbell. If the dumbbell spins like a wheel on an axle, it will not radiate gravitational waves; if it tumbles end over end, as in the case of two planets orbiting each other, it will radiate gravitational waves. The heavier the dumbbell, and the faster it tumbles, the greater is the gravitational radiation it will give off. In an extreme case, such as when the two weights of the dumbbell are massive stars like neutron stars or black holes, orbiting each other quickly, then significant amounts of gravitational radiation would be given off.

So under certain conditions an accelerating mass can radiate gravitational waves. The effect on planetary orbits , though present due to the emission of gravitational waves, is very small , because of the great weakness of gravity.

Gravitational radiation is another mechanism of orbital decay. It is negligible for orbits of planets and planetary satellites, but is noticeable for systems of compact objects, as seen in observations of neutron star orbits.

A: A discussion of the recently observed gravity waves mentioned that the probable cause was two black holes orbiting around their center of mass, each slowing down in its orbit and therefore converting their orbital energy to gravity waves as each moves toward and then away from the point where they are observed.  When the speed at which they approach each other reaches half the speed of light, they emit a big burst of gravity waves as they fall into each other and become one bigger black hole.  
A: There seems to be some ambiguity in the definition of the term, gravity wave.
This reference talks about classic waves in gases and fluids, and I can see how this can effect space time.
But your inference is directly to space-time.  Is space-time a gas, liquid or a solid?  An argument for another time.
I have to agree with levitopher here, the difference is the mass of the object in motion that is creating the gravity wave and the interaction of the forces involved that create the wave.
Examples:
An object moving in a straight line creates a V shapes wave; like a boat,
two black holes orbiting each other create a spiral shaped wave; like a spiral arm galaxy,
and when two black holes merge, a spherical wave would be shaped. think if a rock in a pond, but kind of a poor two dimensional example.
All of this compares space-time to classical wave mechanics which does not necessarily correlate.  All of it is a quick answer off the top of my head, but I hope it points you in the right direction.
