the ainur are created by illuvatar.  then the ainur create the world.  some of the ainur, including the most powerful, go to live in the world.  the two kinds are the valar, the most powerful, and the maiar, who are lesser.  The most powerful of the valar is melkor/morgoth, who tries to thwart the other valar in creating the world, bending it to his own evil purposes.  After a while the other valar get pissed off, sack melkor's fortress, and imprison him for a time.
the elves enter the world.  they are created by illuvatar, not the valar.  the valar eventually convince the elves to come to the valar's land, valinor.  most of the elves never go to valinor.  at that time all the light in the world was emitted by two trees.  the elves become ever more masterful.  eventually, the most powerful elf, feanor, is born, and he crafts 3 jewels, the silmarils, which capture the light of the trees.  then melkor is released.  he plays nice, but poisons the hearts of some of the elves against the valar, including feanor.  melkor then destroys the trees.  at that point they could be revived with the light from the silmarils, but melkor steals those and goes back to middle earth.  feanor swears an oath, as do his sons, that he will not rest as long as someone else, including valar, maiar, and other elves, have the silmarils.  
so they leave.  but there is a giant sea between valinor and middle earth, and the sea elves won't give them ships.  so feanor attacks the elves, the first instance of elf on elf violence.  for this they are cursed, and all that they do will be for their own ruin.  eventually they make it back to middle earth.  feanor and sons had left other elves that were going with them in valinor, then burned the ships.  so the other elves had to brave ice floes in the north.  eventually they fight a battle with morgoth's forces, all the way to the gates of angband, where feanor is killed.  
<going to a review session, back for more synopsis later>