Over the next few days we will hear rumours and speculation as to which team bid what amount. The actual final decision might not be announced until Monday. There are several steps to go through:
Teams submit their bids by 5pm today. The Yankees, red Sox, Rangers, Cubs, Nationals, Mariners and Blue Jays are all expected to bid.
Darvish's team, the Nippon Ham Fighters, evaluate the bids and they can either accept the top bid or decline the top bid. It is 99.99999% certain that they will accept the top bid. However they don't get paid until Darvish signs with a team. The winning bidder migth not be named until Monday.
Once the (Ham) Fighters accept the bid, the winning team and Darvish have 30 days to negotiate a contract. This could fall apart at either end. Darvish is no doubt looking for big dollars. The rumour is that he also would prefer to play for a West coast team. Darvish could choose to not sign and stay in Japan. The (Ham) Fighters would presumably not be happy to have him back.
The two teams could fail to agree on a contract. The posting process favours the selling team. North American teams have to bid high to get the player and that reduces what they are willing to pay the player directly. The player, Darvish, might consider the contract offer to be insulting. Much of the press about Darvish suggests he has a big ego and satisfying him might be difficult. Last season the A's were unable to come to terms with another Japanese player.
So over the next few days there will be many rumours and some facts. Once the winner is announced there will be many more rumours until 11:59pm on the 30th day when a deal might be done.
Jeff Passan from Yahoo Sports has some background here.