Here's some advanced capolytics related to Kirk Hinrich and his Bird Rights.
The typical path for an off-season is for a team to decide if they want to clear cap space in order to sign free agents or stay over the cap and use their Mid-Level Exception. Clearing cap space can also open up a few other avenues like being able to acquire contracts without sending out much in return (see last off-season: Tiago Splitter) as well as re-negotiating current contracts on the roster. Moves of this nature would be considered Salary Cap 101 or possibly 201, they're the straight-forward transactions that a fairly educated fan could figure out.