How are fossils formed?

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Since this is a highly technical question, have you tried searching for academic articles on it?

The one thing I do know is that the conditions required for fossils to form are quite unusual & they only rarely form.

Well, in your knowlege, how are they formed?

Put simply, it's a process of mineralisation - the very slow replacement of the organic tissue, usually the harder parts such as bone, by certain minerals in the surrounding inorganic material.

Important to understand that what paleontologists excavate are not the actual bones of the creature but their mineralised replacement.

And what happens for them immediately after the animal dies?

It's important that a creature's remains are covered or buried quite quickly by ash, mud etc. with certain minerals in it.

Nothing is wasted in nature & practically all that remains of a creature still exposed to the air is consumed & 'recycled'.

So there are many fossils, no?

What exactly do you mean by many fossils? As I said before, fossilisation is quite a rare event. It's only because so many millions of creatures have lived & died that we have the number of fossils we do but the remains of certain species are very scant - just the odd piece of bone-like material in some cases.

The remains of grazing species tend to be more found more frequently simply because of their greater numbers.

So every fossil takes place because of a set series of events?

I'd express it this way - fossils are formed as a result of a certain sequence of events.

That is what I said.

And it is very rare.

The answer to your question is what the entire science of taphonomy is all about 

First, a "fossil" is not simply "bone turned to rock" but any remains of past life that preserve the form but not the substance of the organism (i.e., fossil preservation requires chemical and/or physical alteration of the original remains in whole or part).  So fossils include not only your typical dino but also molds/casts, tracks, burrows, impressions, etc.

Second and importantly, there is no one, single way to make a fossil but many different processes that can occur at different rates even within the same fossil.

Third, to avoid ambiguity of the word "fossil" it's better to speak in terms of preservation and the taphonomic (i.e., preservational conditions and processes) that were involved

These processes and conditions are highly varied and complex but we can generalize into categories:

(a) Casts/molds.

(b) Carbonization: preservation as carbon films via distillation, heat (e.g., most dinosaur feathers are preserved as carbonaceous compression fossils where the original remains have been "carbonized"). 

(c) Permineralization: pore-water percolation with mineral precipitation; most dino "bones" are preserved this way.  The different mineral precipitates include silica, phosphates, carbonates, pyrite, etc.,

(d) Petrification: organic material converted to mineral form.
(e) Replacement: molecule-for-molecule replacement by minerals such as silica (silicification), phosphate
(phosphatization), pyrite (pyritization).

(f) Recrystallization: alteration of bone minerals to thermodynamically stable forms. 

(g) Other (e.g., amber)

A very comprehensive explanation but I fear it's probably wasted on some members who stubbornly persist in claiming that no fossil is more than ten thousand years old!

lol, fair enough