Teflon was discovered with so little research in part because its structure is extremely simple and able to assemble itself without a long series of reactions. Molecular simplicity is also accountable for the material's inert nature and resistance to heat. A carbon atom is covalently bonded to another carbon atom, which is bonded to another, and so forth so that there's a long string of carbons. Since carbon forms four covalent bonds, each carbon in the chain has the two bonds free, which each attach to a fluorine atom. This long string of PTFE arranges its bond angles so each carbon atom is cushioned by its own two fluorine atoms one one side, and the four fluorines belonging to its neighbor on the other, leaving it largely protected from reaction.

Here's a janky ASCII rendition of a few links of PTFE chain. Of course it's actually three dimensional, not flat, so render the angles in your mind to make it look more like a snake and less like a flatworm.

  F   F   F   F   F   F   F   F   F   F   F  
   \ /     \ /     \ /     \ /     \ /     \ 
   -C-     -C-     -C-     -C-     -C-     -C
  /   \   /   \   /   \   /   \   /   \   /  
C-     -C-     -C-     -C-     -C-     -C-   
 \     / \     / \     / \     / \     / \   
  F   F   F   F   F   F   F   F   F   F   F  

Having a uniform cross-section means the molecule is non-polar, adding to its inertia. Also, since other fluorine atoms are the last thing the bonded fluorine atoms want to interact with, PTFE has a very stable crystalline nature. That is, the chains tend to stack together like logs, and due to stability of the carbon center, not twist and braid around one another. The lack of kinks in this crystalline solid makes it even more difficult for other chemicals to react with PTFE, and adds to its famed slipperiness (which, as a point of interest, can be expressed as a coefficient of friction usually between .05 and .20).

The explanation of attaching teflon to other materials given above is somewhat lacking, so I'll try to elucidate on it a bit. One way of making teflon sticky is to bombard one side of the solid with a plasma, the ions of which will tend to break off fluorine atoms on that side. After that, a more "sticky" atom, like oxygen, can be bound onto the exposed carbon chain. This will allow the affected side to adhere to a primer or other substance, as jean-yves mentions above. Sometimes two exposed carbons will bind to each other, forming an unsaturated hydrocarbon. While that may distort the PTFE chain somewhat, the hydrocarbons are nicely sticky and will adhere to other substances.