There are three different kinds of fossils. The first is a part of the actual body of the organism, which has been preserved from decay and which appears just as it was originally.
The second kind is that of the cast or mould of the shape of the plant or animal has been removed.
The third kind is that of the trails of footprints that animals leave behind as they move over the soft mud or clay.
Even the fossils of tiny ants, which lived millions of years ago, can be found perfectly preserved in the amber. When water animals died, their bodies were quickly covered over by mud, which prevented decaying of the shells or skeletons, and hence were well preserved. Some fossils found encased in ice have not only the skeleton but also the flesh and skin well preserved.
Below Fossils info from Wikipedia (Read More):-
Fossils (from Latin fossus, literally "having been dug up") are the preserved remains or traces of animals, plants, and other organisms from the remote past. The totality of fossils, both discovered and undiscovered, and their placement in fossiliferous (fossil-containing) rock formations and sedimentary layers (strata) is known as the fossil record. The study of fossils across geological time, how they were formed, and the evolutionary relationships between taxa (phylogeny) are some of the most important functions of the science of paleontology. Such a preserved specimen is called a "fossil" if it is older than some minimum age, most often the arbitrary date of 10,000 years ago.[1] Hence, fossils range in age from the youngest at the start of the Holocene Epoch to the oldest from the Archaean Eon several billion years old. The observations that certain fossils were associated with certain rock strata led early geologists to recognize a geological timescale in the 19th century. The development of radiometric dating techniques in the early 20th century allowed geologists to determine the numerical or "absolute" age of the various strata and thereby the included fossils.
http://en.wikipedia.org/wiki/Fossils