Here is one way to analyse the sentence:

1. [Adverbial phrase] Now, just three years after the publication of the performance book,

2. [Main clause] I’ve once again taken electronic pen to paper,

3. [Adverbial clause] completing a trading psychology trilogy by focusing on the process of coaching.

Look first for the main clause - it has the main subject ("I") and the main verb that goes with the subject ("have taken"). The commas should help you (though not everyone punctuates well).

1 and 3 both describe the main clause in more detail. Clause 1 does this by stating when it happened. Clause 3 tells us how he has taken pen to paper.

In this case, you could find the main clause quickly because there is no verb in 1 and there is no subject in 3.  

Is this what you wanted?

A trilogy is something that is a set of 3 things, like art, books, movies or similar,  that can either stand alone as a single piece or viewed as one piece.

So in the case of this Author, he has written 3 papers on trading psychology, which focus on coaching.  The reader can choose to read any one paper and they will understand what is being said and hopefully benefit from it.  They can of course just read two of the papers or they can read the three papers. Each paper has its own information and you don`t need to have read the other papers to understand what is being said. 

From any trilogy, however, you get the most benefit, or understanding, from reading, looking at or watching, all three parts of the trilogy in the correct order

Some corrections first...

"How can I improve my grammar comprehension...?" - You need a real subject. It doesn't make sense to ask this question in such an impersonal and abstract way.

"...I've copied from a book..." / "I've completed a trilogy." - Lawrence, it is not good enough to use a simple verb form and hope that the reader understands you. If you're really B2 level, then you ought to know when to use present perfect in basic situations. You are asking about improving your grammatical skills, aren't you?

Moving to a higher level in English isn't only about grammar and vocabulary.  Sharon has already explained the concept of a "trilogy" (this word has a poetic meaning, thus the writer suggests that his/her text on trading psychology is a work of art), and the phrase "take pen to paper" means "to undertake the process of writing".  These are standard English expressions. Once you learn some more, you might find that they are rather colourful. 

If you're wondering about the clause, "completing a trading psychology trilogy...", then you need to study participle clauses. They're very useful.