If you have some time and an Abap editor available, these articles can get you started on Object Oriented programming. The examples are all about local class definitions and using globally defined (standard SAP) class definitions, where the simplest form should be effortless to follow.
Get started - by examples.
Imagine a world, where no FORM routine is needed, ever again. How do you capture the bit of logic you would have captured in a form routine ? Use a method. This simple example shows what you need to define a class LCL_CONTROLLER which controls whatever your report should be doing.
A local class can hold variables, which can be global or instance dependant. Simple example on how to declare a global class variabele on a local class, available from anywhere in your Abap program.
A lot is written and explained on the class instance, instantiating a class or the difference between classes and objects. An object is an instance of a class. Let me lead you to a simple example that demonstrates this. Imagine: cars in a carpark.
SAP's Business Application message logging is made available through the Object Oriented paradigm, which makes it very available indeed. Check out this example on how ready-to-use classes can be used in your coding: