CO₂

1.  Sum the valence electrons for carbon dioxide:
          C = 4        =   4
          O = 6 (x2) = 12
                               16

2.  Form a bond between the carbon and each oxygen: 

3.  We have 12 electrons (16 - 4) remaining after the bonds are drawn.  The distribution of these electrons is determined by a trial and error process.  There are 6 pairs of electrons.  Suppose we try 3 pairs on each oxygen to give:           

We need to check two things:
1.  The total number of electrons.  There are 16 valence electrons in this structure, which is correct.
2.  The octet rule for each atom.  Each oxygen has 8 electrons, but the carbon only has 4.  This cannot be the correct Lewis structure. 
Now we suppose there are 2 shared pairs between the carbon and each oxygen: