Copy highlighted text to clipboard, then use the clipboard to append it to a list

The keyboard combo Ctrl+C handles copying what is highlighted in most apps, and should work fine for you. This part is easy with pyautogui. For getting the clipboard contents programmatically, as others have mentioned, you could implement it using ctypes, pywin32, or other libraries. Here I've chosen pyperclip:

import pyautogui as pya
import pyperclip  # handy cross-platform clipboard text handler
import time

def copy_clipboard():
    pya.hotkey('ctrl', 'c')
    time.sleep(.01)  # ctrl-c is usually very fast but your program may execute faster
    return pyperclip.paste()

# double clicks on a position of the cursor
pya.doubleClick(pya.position())

list = []
var = copy_clipboard()
list.append(var) 
print(list)

Example using tkinter:

from tkinter import Tk
import pyautogui as pya

def copy_clipboard():
    root = Tk()     # Initialize tkinter
    root.withdraw() # hide the tkinter window
    pya.hotkey("ctrl", "c") # copy the text (simulating key strokes)
    clipboard = root.clipboard_get() # get the text from the clipboard
    return clipboard

copy_text = copy_clipboard()
print(copy_text)

Tk().clipboard_get() returns the current text in the clipboard.

What soundstripe posted is valid, but doesn't take into account copying null values when there was a previous value copied. I've included an additional line that clears the clipboard so null-valued copies remain null-valued:

import pyautogui as pya
import pyperclip  # handy cross-platform clipboard text handler
import time

def copy_clipboard():
    pyperclip.copy("") # <- This prevents last copy replacing current copy of null.
    pya.hotkey('ctrl', 'c')
    time.sleep(.01)  # ctrl-c is usually very fast but your program may execute faster
    return pyperclip.paste()

# double clicks on a position of the cursor
pya.doubleClick(pya.position())

list = []
var = copy_clipboard()
list.append(var) 
print(list)