I would like to learn something more about NoSQL databases, so I've chosen to create a new project from scratch to handle football results. In my traditional relational database, I have tournaments, teams, results and class tables. All are obviously related.
What might be a good approach for designing a project like this, using a NoSQL approach instead?
Use the right tool for a particular job. By asking this, it's clear you don't know when NoSQL is appropriate for data storage. A lot of people are using NoSQL just because it is the "thing of the moment". Usually NoSQL databases have no schema and should be used when the data is better represented by its model. You should not use a NoSQL database to store data that is typically relational; a relational database should be used in that case. I know that when there is a need to scale the application to be capable of handling millions of transactions then NoSQL model works better (even when the data is relational), but I think that is not your case.
First, there are clearly defined usecases for using NoSQL over a traditionnal RDBMS. Make sure your system meets one or more of these criteria before jumping into NoSQL, or else you could run into problems.