You will want to pass pyperclip.paste()
the same place you would place a string for your entry or text widget inserts.
Take a look at this example code.
There is a button to copy what is in the entry field and one to paste to entry field.
import tkinter as tk
from tkinter import ttk
import pyperclip
root = tk.Tk()
some_entry = tk.Entry(root)
some_entry.pack()
def update_btn():
global some_entry
pyperclip.copy(some_entry.get())
def update_btn_2():
global some_entry
# for the insert method the 2nd argument is always the string to be
# inserted to the Entry field.
some_entry.insert(tk.END, pyperclip.paste())
btn = ttk.Button(root, text="Copy to clipboard", command = update_btn)
btn.pack()
btn2 = ttk.Button(root, text="Paste current clipboard", command = update_btn_2)
btn2.pack()
root.mainloop()
Alternatively you could just do Ctrl+V :D