You have to do it on the phone, you could probably hold your trip online and then call to pay for the trip and request an upgrade at the same time if it matters, otherwise just book the flights and then call to make the request.
You will probably be put on a wait list depending on your status and the demand. If you have status you may look out for the $ upgrade offers AA will send you after you book, to the detriment of EPs hoping for a free upgrade they are have been giving away $ upgrades for a song the past year (be patient) but I think that you have to have status to qualify for the offers (may be wrong).