OK, here goes!  (2nd time, had to delete some extra dots in my first draft!)

 

Lewis dot structures are the "first tier" for describing covalent bonding in molecules.  The general method was first published by Gilbert Lewis in 1916, so it's an oldie but still a goodie.  Our knowledge is much greater now but we still use the Lewis structures all the time because they are generally easy to write and they usually give the correct picture of the molecule in terms of how the atoms are connected together, the types of bonds present (single, double, or triple) and the numbers of "lone pairs" of electrons on the atoms.

 

Here is the general approach I teach to my students.  I'll take the molecule sulfur dioxide, SO2, as an example.

 

1.  Add up the total number of valence electrons of all the atoms in the molecule.

 

Valence electrons are the outermost electrons in the atom.  Therefore, these electrons are the ones that will be interacting with valence electrons of other atoms, forming bonds.  You can get the number of valence electrons of an element from the periodic table - it is simply the group number of the group the element is in.  Sulfur is in group 6A (or "VIA" or in some tables (European) "6B" or "VIB"), so it has 6 valence electrons.  By the way, there is a newer group labeling scheme that just numbers the groups from left to right 1 to 18, so S would be in group 16 in that case, the last digit gives the number of valence electrons in that case.

 

1 sulfur:     1 x 6 =   6  valence electrons
2 oxygens: 2 x 6 = 12 valence electrons
                              --
                             18 valence electrons total in the molecule

 

2.  If you have a "unique" atom (only one) try putting it in the middle and attaching the other atoms to it starting with single bonds.

 

   O-S-O

 

   or using dots for the electrons in the bonds,

 

   O:S:O

 

A line represents two electrons, so a single bond always contains two electrons.  You can use dots instead, but using lines for bonds is usually neater.

3.  Now fill in enough dots around all of the atoms to get 8 electrons total around each atom.  (I hope these structures show correctly!)
    ..    ..    ..
   :O---S---O:
    ..    ..    ..

 

  or with dots only,

    ..    ..    ..
   :O : S : O:
    ..    ..    ..

 

The purpose of this is to satify the "octet rule" which says atoms will try to obtain 8 valence electrons by sharing electrons with other atoms (the case here) or by gaining or losing electrons (forming ions in ionic compounds like NaCl).  This is a particularly stable arrangement, the same number of electrons the noble gases have (except for helium, it has only two).  One exception is hydrogen - it will only have two electrons in a compound (to be like the noble gas nearest it, helium).

 

When you put electrons in like this, be sure they are clearly paired on the top, bottom, left, or right of the atoms in your drawing.  Never scatter them randomly around the atoms.

4.  Is this structure OK?  Often at this stage it is, but here's how we'll check:  Add up all the dots in the structure and compare the total with the number we got in step 1, 18 total valence electrons.  Oooops, we have 20, two too many!  But if we remove two dots, we can't get 8 around each atom.  What do we do next?

5.  Put a double bond in place of one of the single bonds:

 

   O=S-O   or   O-S=O     (the double bond can be on either side)

 

   or using dots to represent the bonding electrons,

 

   O::S:O  or   O:S::O

 

Now fill in enough electrons to have 8 electrons around each atom and recheck the total.

   ..     ..    ..           ..    ..   ..
   O==S---O:    or   O :: S : O:
   ..           ..           ..         ..

Bingo!  We have 18 electrons represented in our structure, the correct number.  Done.  This is indeed the correct dot structure of SO2.

Lone pairs are simple pairs of electrons (dots) that are not making a bond, but are needed to complete the octet on the atom.  Bonding pairs are pairs of electron being shared between the atoms forming a bond.  I prefer to use lines for bonding pairs and dots for nonbonding pairs (lone pairs) to make a cleaner drawing.

 

Well, this is a start, hope it helped a little!  Of course, practice make perfect.  As you do more, you will run into some less clear cases where you may have more than one possible stucture that seems to work, or you may run into cases that don't obey the octet rule on all atoms or have an odd number of electrons.  Then it will be more difficult to judge what the best structure is, but there are some guidlines for these cases too, such as making the formal charges on all atoms as close to zero as possible.  But the rules outlined above still apply, and they certainly work well for most molecules.