Tkinter has three geometry managers: pack, grid, and place.
Pack and grid are usually recommended over place.

You can use the grid manager's row and column options
to position the Scrollbar next to the Text widget.

Set the Scrollbar widget's command option to the Text's yview method.

scrollb = tkinter.Scrollbar(..., command=txt.yview)

Set the Text widget's yscrollcommand option to the Scrollbar's set method.

txt['yscrollcommand'] = scrollb.set

Here's a working example that makes use of ttk:

import tkinter
import tkinter.ttk as ttk

class TextScrollCombo(ttk.Frame):

    def __init__(self, *args, **kwargs):
        
        super().__init__(*args, **kwargs)
        
    # ensure a consistent GUI size
        self.grid_propagate(False)
    # implement stretchability
        self.grid_rowconfigure(0, weight=1)
        self.grid_columnconfigure(0, weight=1)
        
    # create a Text widget
        self.txt = tkinter.Text(self)
        self.txt.grid(row=0, column=0, sticky="nsew", padx=2, pady=2)

    # create a Scrollbar and associate it with txt
        scrollb = ttk.Scrollbar(self, command=self.txt.yview)
        scrollb.grid(row=0, column=1, sticky='nsew')
        self.txt['yscrollcommand'] = scrollb.set

main_window = tkinter.Tk()

combo = TextScrollCombo(main_window)
combo.pack(fill="both", expand=True)
combo.config(width=600, height=600)

combo.txt.config(font=("consolas", 12), undo=True, wrap='word')
combo.txt.config(borderwidth=3, relief="sunken")

style = ttk.Style()
style.theme_use('clam')

main_window.mainloop()

The part that will address your Scrollbar being small is sticky='nsew',
which you can read about → here.

Something that will be helpful for you to learn right now is that different Tkinter widgets can use different geometry managers within the same program as long as they do not share the same parent.

The tkinter.scrolledtext module contains a class called ScrolledText which is a compound widget (Text & Scrollbar).

import tkinter
import tkinter.scrolledtext as scrolledtext

main_window = tkinter.Tk()

txt = scrolledtext.ScrolledText(main_window, undo=True)
txt['font'] = ('consolas', '12')
txt.pack(expand=True, fill='both')

main_window.mainloop()

The way this is implemented is worth taking a look at.

Note that you must define yscrollcommand=scroll.set in the Text widget, and configure the scrollbar using the line: scroll.config(command=eula.yview) Here is your code, rewritten with one scrollbar:

# Import Tkinter
from Tkinter import *

# define master
master = Tk()

# Vertical (y) Scroll Bar
scroll = Scrollbar(master)
scroll.pack(side=RIGHT, fill=Y)

# Text Widget
eula = Text(master, wrap=NONE, yscrollcommand=scroll.set)
eula.insert("1.0", "text")
eula.pack(side="left")

# Configure the scrollbars
scroll.config(command=eula.yview)
mainloop()

Here is a Tkinter example with two scrollbars:

# Import Tkinter
from Tkinter import *

# define master
master = Tk()

# Horizontal (x) Scroll bar
xscrollbar = Scrollbar(master, orient=HORIZONTAL)
xscrollbar.pack(side=BOTTOM, fill=X)

# Vertical (y) Scroll Bar
yscrollbar = Scrollbar(master)
yscrollbar.pack(side=RIGHT, fill=Y)

# Text Widget
text = Text(master, wrap=NONE,
            xscrollcommand=xscrollbar.set,
            yscrollcommand=yscrollbar.set)
text.pack()

# Configure the scrollbars
xscrollbar.config(command=text.xview)
yscrollbar.config(command=text.yview)

# Run tkinter main loop
mainloop()