To be able to take part in the ranked mode, you need to complete the first two chapters in the story mode. This means, you need to complete 10 battles. Seasons can vary in duration so make sure you take part as soon as it starts.
By clicking on the info button next to “ranking” you will see the current ranking and which league you are a part of by clicking on “league/season”. There you will also be able to see the points you receive, your level-up rewards and the season rewards.