What are the main steps I can follow in improving my English communication skills?

If you are asking about written communication, you are perfectly good because the way you've framed this question tells you are skilled. If you are hesitant in speaking and feel you need to improve, speaking more in English is the answer. But again, maybe by "communication skills" you don't mean language part but the skills of persuasion and effective speech. That come through training. Business schools do that. As regards linguistic skills, proper pronunciation and fluency comes if you converse with people who are good at that. Language is a practical art, the more you practice, the better it is.   

Listen, read and communicate as much as possible.

communication with native english speakers and or english speakers, and never be shy to practice 

Relax.Listen properly don't hear.Focus.

Read English stories and newspapers.

Communicate as much as you can with any natives 

I think that the most important aspect of communicating is to go out and actually "communicate" with others, natives or otherwise, and not be shy about it. Fear is a terrible thing to hinder one's self from being able to speak flawlessly and fluently, but it's a big factor. You need to shed the fear aside and communicate, talk, speak, negotiate, and all those things.

If it is written communication, i will suggest you undergo training centered on art of communication,also by doing self reading both offline and online. Journals on business communication and other text will be of great help

RIGHT OR WRONG YOU KEEP ON SPEAKING WITH PEOPLE WHO ARE BETTER IN COMMUNICATION. SLOWLY YOU WILL PICK UP WITH GOOD COMMUNICATION IN ENGLISH.BUT THIS IS NOT END., YOU WILL FIND BETTER COMMUNICATING PEOPLE THAN YOU AT EVERY MOMENT OF LIFE., SO KEEP ON DEVELOPING YOUR SKILLS DAY BY DAY.IN MY VIEW GOOD COMMUNICATION IS  GOOD LEARNING.

watch more and more english movies with subtitles...  concentrate on subtitles and try to repeat it... otherwise as usual read more books... 

First you have to be determine on learning. Learning English is fun and easy.

listening music & watching series that are interested to watch without subtitle is very helpful plus communicate with native speakers. you have to try speaking in English even if you had lots of mistakes ,it's ok! by time  you'll be able to speak correctly. 

Listen to English Music and Watch movies with subtitles , it is very very effective and if you can back those steps with some basic english grammer.It would be great