The league runs over 14 days with 13 matchdays where each team per match day typically will play one home match and one away match.
The last day of the season (day 14) is not a matchday, but on this day you can catch up and play all the matches which has not been kicked off yet. After day 14 the seasons ends. In total up to 26 matches are played before the league ends.

League level 1-5
#1 wins the title, a league trophy and a cash prize
Top 4 qualifies to play Champions League in the following season
Top 7 promotes to a higher league
#13+14 relegates to a lower league

All managers start at league level 1. When promoted you advance to league level 2 and so on. 

When you promote from league level 5 you enter the Super League. You start at the lowest super league level - e.g. SL3 and if you promote you promote to SL2. When you promote from SL1 you get promoted to The Premier Division which is the highest league level in the game.

Super League
#1 wins the title, a league trophy and a cash prize
Top 4 qualifies to play Champions League in the following season
Top 2 promotes to a higher league (unless you are in Premier Division)
#13+14 relegates to a lower league

If matches has not been kicked off the league will end with these matches as unplayed. So some clubs might have fewer matches than 26 played when the league ends. So make sure you always play all your matches before the season ends.

NOTE!
Sometimes teams go inactive in the higher league. To fill the league system, extra clubs are promoted. That is why sometimes more are promoted than stated above and also why sometimes not all relegated teams actually gets relegated.