Help me understand this... (Classes and self).

[Larz60+]

I am trying to understand the process by which widgets are added to the GUI using classes in this manner.

You really should spend some time learning about classes in general.
a widget is a class as a matter of fact everything in python is a class
To show this, consider this example:

>>> a = 5
>>> type(a)
<class 'int'>
>>>

a is an instance of class int
as for widgets:

>>> import tkinter
>>> root = tkinter.Tk()
>>> type(root)
<class 'tkinter.Tk'>
>>> label_a = tkinter.Label(text='abc')
>>> type(label_a)
<class 'tkinter.Label'>
>>> # If you want to see methods and attributes for Label:
>>> help(tkinter.Label)
...

here are some tutorials on classes:
Class Basics
Class Intermediate: Inheritance
Class Intermediate: Operator Overloading
Classes [advanced]: Dependent attributes (and Descriptors)
Classes [advanced]: Descriptors (managed attributes)