From A guide to naming organic compounds. This is Section 5.

Putting what we have learnt all together
Having read the other writeups in this series, we now need to know what to do when you have a functional group hanging off a hydrocarbon with geometric isomerism, for example. It's not that hard, really!

    Cl  H   H   H   H   H
    |   |   |   |   |   |
H - C - C - C - C - C - C - C = O
    |   |   |   |   |   |   |
    H   H   H   H   H   H   H

One thing that I didn't mention in my functional groups writeup is the fact that you can have two or more functional groups attached to a chain, even a single carbon atom in a chain. Anywhere where something can bond can potentially have a functional group. So, the above molecule has a chain of length 7, the double bonded oxygen on the end makes it an aldehyde, and the chlorine on the other end means it has the prefix chloro-. So, the name of this molecule is this:
1 - chloroheptanal.
But how about this one?
                                    H
                                    |
    H   H   H   H   H   F   H   H - C - H
    |   |   |   |   |   |   |       |
H - C - C - C - C - C = C - C - O - C = O
    |   |   |   |           |       
    H   H   H   H           H       
That one's crazy!! But lets break it up into something easier to work with...

R-C=O
  |
  O-R'

Where R represents:

    H   H   H   H   F   F   H
    |   |   |   |   |   |   |      
H - C - C - C - C - C = C - C
    |   |   |   |           | 
    H   H   H   H           H

and R' represents:

     H
     |
 H - C - H
     

Just like in the functional groups writeup, we can just break it up, name the bits and then put it all together. So, we can easily see that the molecule is an ester with a methyl group at R, all we have to do now is name the R' part, and that's easy! It has 7 carbons in the chain, some cis isomerism with some fluorines. We number the carbons so that the important carbons have lower numbers:
    H   H   H   H   F   F   H
    |   |   |   |   |   |   |      
H - 7 - 6 - 5 - 4 - 3 = 2 - 1
    |   |   |   |           | 
    H   H   H   H           H
So the name of this part is cis - 2,3 - fluoroheptene. And, putting the names together we get cis-2,3-fluoroheptenyl-methanoate (RGroup-R'Group-oate). See - Not that hard...

Some things I forgot to mention: Cyclic stuff!! How could I forget?
Imagine this:

    H   H
    |   |
H - C - C - H
    |   |
H - C - C - H
    |   |
    H   H
Hmm...4 carbons connected in a ring? That's probably a but- thing of some sort. Well, in fact, it's called cyclobutane! These wonderful rings have their own special properties and subtlties about them, but the naming conventions are essentially the same. I'll give you an overview:

                 Cl
         |  \ /  |
   - C = C - C - C - Cl

     |           |
    \             /
     C           C
    /             \
     |           |  F

   - C - C - C - C -
     |  / \ / \  |

(I've not drawn the hydrogens...)
So, we have a cyclodecene with come halides hanging around. To name it, we want the special stuff to have low numbers, with the double bond being the lowest. So, we make the double bond bond number 1 and count around:

                 Cl
         |  \ /  |
   - 1 = 2 - 3 - 4 - Cl

     |           |
    \             /
     10           5
    /             \
     |           |  F

   - 9 - 8 - 7 - 6 -
     |  / \ / \  |

(I've not drawn the hydrogens...)
So, the name of the above ring is 4,4-dichloro, 5-fluorocyclodec-1-ene. But the position of the double bond is obvious, so 4,4-dichloro-5-fluorocyclodecene would suffice.

Benzene Check this out:

      C = C
     /     \
    C       C
    \\     //
      C - C
(I've not drawn the hydrogens in...One for each carbon)

Above is a benzene ring. It is the most stable of the cyclic compounds and therefore has a special name: Benzene. Benzene is not usually drawn this way because the bonds are actually shared across the carbons so, in effect, they are 1.5 bonds (rather than alternating single and double bonds). This means that often you'll see benzene drawn as a hexagon with a circle in the centre.
When naming compounds containing a benzene ring, all of the normal rules apply, but rather than trying to name that strange hexene ring, call it benzene, or, if it is a side group, it is also known as phenyl.

Well, that essentially covers everything that I remember about organic chemistry. Please if I have left something important out, tell me!

Professor Pi helped out alot with this writeup. I thank him.