Is is correct to write: 'Author Martin Amis describes...', or should we use the article 'the' in front of 'author'?
"The" is not required.
There are many examples where a profession is prefixed to a name. For example:
Driver Lewis Hamilton came in first once again.
However, I'm quite sure that it is context dependent. For example, let us say we are talking about your author describing a door.
Author Martin Amis describes the door as unbreakable.
is slightly different to
The author, Martin Amis, describes the door as unbreakable.
So pick whichever one you need.
Both are possible, but I think the difference is one of formality. Author Martin Amis might be found in a popular newspaper, but a piece of academic prose would be more likely to refer to the author Martin Amis, assuming it wasn’t enough simply to write his name alone.
It's actually a property of a word whether it can be used this way or not. Compare:
Author Kate Gregory recommends C++ AMP because ...
Sheep Dolly was cloned...
Author can be anarthrous and sheep can't. Just about every profession a person can hold is ok to use without "the" and as for all the other nouns in English, I don't think there's really a rule. Off the top of my head, all the examples I can find are nouns describing something a person is. I mean that nouns like table, blizzard, whisper, and so on can't be used like this, while schoolboy, housewife, candidate, and so on all can. But I'm not sure that's a rule, it might just be that my imaginary sentence generator is slow this morning.
Hurricane Sandy swept into New York
Not sure why that's ok and Sheep Dolly isn't.