It is useful to distinguish between the restoration and reconstruction of fossils. The first is the process of 'filling in the gaps' in fossil material, whereas the second is the process of inferring their former appearance as living organisms.

Restoration of fossils is mainly restricted to fossil vertebrates; in the case of fossil invertebrates, complete specimens are usually common enough for reconstructions to be unnecessary. In vertebrates it is extremely rare for every bone to be preserved, and in many cases a palaeontologist has only 20-30% of a skeleton on which to work. Reasons for restoring skeletons include the desire to have complete specimens for display, and the desire to better understand how the animal functioned.

Because vertebrates are bilaterally symmetrical, if a bone is missing on only one side of the skeleton it is possible to make a mirror image to serve as a stand-in. If a fossil is closely related to a better known species, be they living or also fossil, the better known form can serve as a guide. This becomes technically more difficult if the fossil to be restored differs significantly in size from the better known form. In that case, an allowance must be made for changes in proportions as the organism becomes larger. Such changes are referred to as allometry, literally 'other measurements'. For example, limbs become stouter as animals become larger. Consider the limbs of a gazelle and an elephant. A gazelle that evolved to have the mass of an elephant would have to have limbs as stout, otherwise the bones would break. These relationships are well understood and valid allowances are made in a straight forward manner by plotting measurements on logarithm-logarithm paper. The Museum of Victoria's cast of the giant goanna Megalania prisca was restored in just this manner.

The problem of restoring fossils:

'Any scene from deep time embodies a fundamental problem: it must make visible what is really invisible. It must give us the illusion that we are witnesses to a scene that we cannot really see; more precisely, it must make us 'virtual witnesses' to a scene that vanished long before there were any human beings to see it.'

From the introduction to Rudwick, M. J. S. 1992. Scenes from deep time. Early pictorial representations of the prehistoric world. University of Chicago Press.

The process of making two- or three-dimensional fossil reconstructions is an important part of palaeontology in museums. The process has a number of stages. Firstly, the artist and scientists meet to discuss what is required, and to examine the original fossil material. The artist then spends a lot of time just thinking about the commission. How should the organisms central to the reconstruction be placed and posed in their habitat? What other organisms should be shown with them either in the foreground or background? What season of the year, time of day, and weather conditions are to be portrayed? What is the physical habitat? Given those factors of the setting, are there particular properties of light in that environment that must be taken into account? Should one individual be illustrated or a group? If a group, what kind of interaction should be shown between individuals? What is the health of the organism or organisms to be portrayed?

To answer these questions, the artist first reconstructs the skeletal structure from the remains preserved in the fossils. The soft anatomy of muscles and flesh covering the bones is not preserved in the fossils, though the scars where muscles were attached to the bones may be preserved. The muscle masses that would have linked the various bones are reconstructed from these scars, as well as from study of the muscle placement in the closest living relatives of the animal. Finally, skin is placed on the muscle masses and a texture and colour pattern given to it, or the fur or feathers which covered it are reproduced. That is done by studying the colour patterns of the nearest living relatives. If the reconstruction is a two dimensional painting, the artist may sculpt a reconstruction of the animal in clay and then work from that in order to get the perspective precisely right.

To reproduce the setting for the organisms central to the reconstruction, the artist may visit similar modern habitats. Experiments may be performed; e.g. freezing leaves in shallow water to see what their appearance is like when reconstructing a polar pond scene.

Information provided by: http://www.museum.vic.gov.au