I have been given the class names, properties, and methods. 
I’m not sure what the relationships are between them, so I’d appreciate it if someone can correct me below before I start drawing:
Games has a one to many relationship to Sport. Sport has a one to many relationship with Event.
Event has a one to many relationship with Race.
And Heat and Final are subclasses of Race.
What do you think?
What you have sounds like a pretty good foundation – I think you’ve captured the relationships pretty well. It seems to me to more of a data model than a class model per sé.
To fill your class diagram out, ask yourself the following questions:
Post your solution in the question so we can see what you come up with 🙂