I was reading this thread about the Lakers signing Steve Blake, and saw several people, including much to my surprise both the current and former Editors-in-Chief of Silver Screen and Roll, curious and confused as to how the Larry Bird Exception works, specifically on the case of how it works on Derek Fisher (LA can sign him to the Max if they want, guys). I began typing this out as a reply to C.A's question, and then decided I may as well make it a Fan Post to serve as a point of reference whenever questions are raised about the Larry Bird exception. If you have any further questions on Bird Rights, or on the Cap rules in general, feel free to ask down below in the comments.
The Larry Bird exception was designed to allow teams to keep their own long-term players and not lose them to free agency. It is named as such because Larry Bird was the first player it was used to retain.
The Larry Bird exception is a Cap exception that allows teams to disregard the Cap when signing players they have Larry Bird rights to - they can sign them for any amount up to the Maximum. It is independent from the MLE, Minimum, Bi-Annual and other exceptions, and can be used as many times as a team wishes, provided they have the Bird Rights to that player, there is no limit to Bird Rights contracts per year or anything. As with all other exceptions, if a team is under the Cap, the team may only use Cap Space OR the exception, not both.
The Larry Bird Exception is a Cap Exception, but NOT exempt from the Luxury Tax - if a a team is already over the Luxury Tax Threshold, or if a signing under the Larry Bird Exception places them over the threshold, they will have to pay a dollar-for-dollar tax on every dollar they spend over this threshold.
Rules such as the Larry Bird Exception are what allow the Lakers to be so far over the Cap but still resign and/or extend their own players such as Lamar Odom, Kobe Bryant, Pau Gasol, Andrew Bynum and hopefully Derek Fisher.
Teams have Bird rights on any player that has been on their roster for three years or more. Bird Rights are transferable through trade - Eg, if the Lakers trade Sasha, whose Bird rights they possess, to another team, that team then possess his Bird Rights and can re-sign him for 2011 regardless of their Cap situation. Bird Rights are lost as soon as a player switches teams through Free Agency - though I think they can be retained through sign and trade.
Something that I am sure you all have heard about, the fact that Dwyane Wade and LeBron James can earn up to $30 million extra if they resign with their respective teams, as well as having another year on their deal, is also a subset of the Larry Bird rule manufactured to give teams an advantage in retaining their own players.
The Lakers this offseason possess both the Bird Rights of Derek Fisher, Jordan Farmar and Shannon Brown, meaning they can re-sign them for absolutely any amount they wish up to the Maximum allowed contract by the NBA. The Lakers are already over the Luxury Tax Threshold, however, and thus every dollar spent on contracts will still count towards the dollar-for-dollar Luxury Tax.
There is also another form of Bird Rights, the 'Early Bird Exception', which applies to players that have been on the same team for 2 years. It is similar to Bird Rights, except the maximum value of a contract over the cap using the Exception is the same value as the MLE of that year - though using the Early Bird Exception does NOT forfeit a team the use of their MLE.
Because of an incident in the '90s, where a team that was over the Cap offered their Early Bird Exception to a free agent who had played for them the prior two years, but still were not able to retain the Free Agent because another team offered a larger deal and the team with the player's Early Bird Rights were not able to match due to not being able to exceed MLE-value, other teams cannot offer a player who is under the Early Bird Exception any contracts greater than MLE value.
The Lakers currently possess the Early Bird Rights to Josh Powell and DJ Mbenga, meaning they can re-sign them regardless of their Cap scenario to any amount up to the Mid-Level Exception (though they will pay Luxury Tax on every cent of their contracts), and no other team can exceed the value of the Mid-Level Exception in an offer to them.
Disclaimer: All this information is off the top of my head, remembered from a Larry Coon article I read over a year ago. Considering this, there may be some small errors of detail, but the basic Cap rules are 100% correct.