How do I become chess world champion? If I play better than the current world champion, Carlsen, and I am able to win him - how would I do to become world champion as fast as possible? Would I have to go through long tournaments or is it enough to consistently beat the world champ?

If that is the case, I wonder why Vassily Ivanchuk isn't the world champion?
The rules for becoming world champion have changed over the years and might very well change in the future. 

With the current rules, in order to become chess world champion, you have to beat the reigning world champion in a match over 12 games and potentially (if the score is 6-6) additional tie-break games. The next match will be in 2018. Rules for this FIDE World Championship Match are found in the FIDE Handbook

In order to qualify for this match for the world championship you have to win the Candidates Tournament. The following qualify for the next Candidates Tournament according to the FIDE Rules and Regulations:


Sergey Karjakin (as runner-up of the previous WC match),
the first two of the FIDE World Cup 2017, 
the first two of the FIDE Grand Prix 2017, 
the two highest rated players who are not otherwise qualified and who have participated in the FIDE World Cup or FIDE Grand Prix
one player nominated by the organizer with a rating of at least 2725 in 2017


Some more detail regarding the Candidate tournament you can find in this question and answers

What is the quickest way to the Candidate tournament?

If you are just starting out with chess, it will take you many years to reach a level of 2725 (required for the organizer wildcard) or of being among the highest rated players not qualified otherwise (which would be in the 2800 range).

Qualification for the FIDE Grand Prix is also aimed at top level players. If you are interested you can read about it here

There are many ways to get to the FIDE World Cup (see here) including winning continental championships. If you are from a part of the world where chess is not all that popular, qualifying as IM is not impossible. In any case this seems to be the easiest route for getting to the Candidates Tournament.