Q: How to write button callback? Below is the code that I am using to make a chessboard out of buttons.
from Tkinter import *

for x in xrange(8):
    for y in xrange(8:
        if((x+y)%2 == 0):
            Button(root, bg="white", width=11, height=5).grid(row=y, column=x)
        else:
            Button(root, bg="black", width=11, height=5).grid(row=y, column=x)

I know how to make a callback function for an individual button, but I am not sure how I would go about implementing a callback function for each of these 64 buttons so that, when pressed, they will return their position in the grid.

A: def callback(event):
   x,y = event.widget.grid_location()

This example should point you into the right direction.
update:
to clarify the usage of grid_location i did a quick-google and found ... a SO-post ;-)
which put me to shame by providing exactly your needed solution in a more direct way:
grid_info = event.widget.grid_info()
print "row:", grid_info["row"], "column:", grid_info["column"]

so the credit should go to Bryan Oakley ;-) and this question may be called a duplicate ...

A: Try binding the x and y values for each button to a lambda that can call a handler function whenever a button is pressed. Now you have the x and y position of each button press.
def handlebuttonpress(x,y):
  print 'Button x-{0} y-{1} pressed'.format(x,y)

width, height = 8, 8
for x in xrange(width):
  for y in xrange(height):
    if((x+y)%2 == 0):
        Button(root, command=lambda x=x, y=y: handlebuttonpress(x,y), bg="white", width=11, height=5).grid(row=y, column=x)
    else:
        Button(root, command=lambda x=x, y=y: handlebuttonpress(x,y), bg="black", width=11, height=5).grid(row=y, column=x)


A: Edit: I think I like @DonQuestion's event-based approach better because it does not require a different function for each button. 
Below I've adapted my original code to use 
    master.bind("<Button-1>", self.onclick)

to react to mouse clicks (instead of using tk.Button(command = ...)

import Tkinter as tk

class ButtonEventBlock(object):
    # http://stackoverflow.com/a/6102759/190597
    def __init__(self, master, names, cols):
        self.names = names
        self.cols = cols
        self.button = []
        for i, name in enumerate(names):
            self.button.append(tk.Button(master, text = name))
            row, col = divmod(i, self.cols)
            self.button[i].grid(sticky = tk.W+tk.E+tk.N+tk.S,
                                row = row, column = col, padx = 1, pady = 1)
        master.bind("<Button-1>", self.onclick)

    def onclick(self, event):
        info = event.widget.grid_info()        
        # print(info)
        # {'rowspan': '1', 'column': '3', 'sticky': 'nesw', 'ipady': '0', 'ipadx':
        # '0', 'columnspan': '1', 'in': <Tkinter.Tk instance at 0xab3d7ec>,
        # 'pady': '1', 'padx': '1', 'row': '0'}
        row, col = [int(info[key]) for key in ['row', 'column']]
        i = self.cols*row + col
        print(row, col, self.names[i])

names = ('One', 'Two', 'Three', 'Four', 'Five',
         'Six', 'Seven', 'Eight', 'Nine', 'Ten')

root = tk.Tk()
ButtonEventBlock(root, names, cols = 5)
root.mainloop()


