Avogadro's number is officially defined as the number of particles 
in 12.0 grams of Carbon-12 (carbon that has 6 protons and 6 neutrons in 
its nucleus).  The accepted value today is approximately 6.0221367*10^23, 
and with the equipment available to a modern chemist there are several 
ways to arrive at this number.

	A chemist could use a mass spectrometer, a precise instrument 
which can determine an element or compound's mass.  We won't go into 
details, but such a device is sensitive to the number of atoms present, 
and it could be used for "atom counting."  Of course, a chemist wouldn't 
count out an entire mole of atoms, but could count a small amount and then 
using proportions could find out how many atoms are in a mole.

	Also, one could use the theory behind Brownian Motion to calculate 
Avogadro's number.  Albert Einstein did this successfully in 1905.  
Brownian Motion occurs when small solvent molecules collide with larger 
solute molecules.  (You can observe this by placing a drop of milk under a 
microscope).  

	Finally, one could determine Avogadro's number using x-rays.  By 
examining how x-rays bounce off of a crystal, a chemist can tell how atoms 
in the crystal are spaced.  By using the density of the crystal and the 
fact that density = mass/volume, one can calculate Avogadro's number.  The 
actual formula used is the following:

Na = (nM)/(pV)

	In this case Na = Avogadro's number, n is the number of atoms in a 
crystal cell, M is the molar mass of the element, p is the element's 
density, and V is the volume of a cell.  A cell is the smallest repeating 
structure of a crystal.

	Also, you can check the following site for more information and 
additional methods for calculating Avagadro's number:
 http://www.madsci.org/posts/archives/jan99/916465856.Ch.r.html

	Any college level text book will also contain information on at 
least one method of calculating Avogadro's number.