That part can take a while to sort out because it's not like American sports where there's a season and then a playoff at the end. Each league and tournament is a distinct competition, and can be in two or three at a time.
In club football, these are the four types of competition that you'll encounter most often:
- Domestic league (Barclay's Premier League, Liga BBVA, Ligue 1, Serie A, etc.)
- Domestic cup (FA Cup, Copa del Rey, etc,)
- League cup (Capital One Cup)
- Continental competition (UEFA Champions League, UEFA Europa League, etc.)
I was never able to sort it all out until I picked the club that was going to be
my club. I think that helps unravel the calendar a little bit. Before I did that, I just tried to follow American players abroad and watch matches as a neutral, and it all ran together for me. If you haven't picked a league or a team to follow yet then doing so would probably help a lot. After that, just focus first on following them in their domestic league. If you can keep up with that, the other stuff will come around.