I have been programming in C# and Java for a little over a year and have a decent grasp of object oriented programming, but my new side project requires a database-driven model.
The big question: how can you get your head around it? It just takes practice. You try implementing a database design, run into problems with your design, you refactor and remember for next time what worked and what didn't.
To answer your specific questions... this is a little bit of opinion thrown in, as in "how I would do it", not taking into account performance needs and such. I always start fully normalized and go from there based on real-world testing:
Table Event
EventID
Title
StartDateTime
EndDateTime
Table ShiftEvent
ShiftEventID
EventID
ShiftSpecificProperty1
...
Table Product
ProductID
Name
Table Category
CategoryID
Name
Table CategoryProduct
CategoryID
ProductID
Also reiterating what Pierre said - an ORM tool like Hibernate makes dealing with the friction between relational structures and OO structures much nicer.