Firing squad...hehe!
"Congress shall have the power...To define and punish Piracies and Felonies committed on the high Seas, and Offences against the Law of Nations"
Pursuant to the power to define and punish offences against the law of Nations, I would imagine that the authorization to use military force to apprehend Al Qaida terrorists includes the ability of said forces to convene courts martial in areas subject to their jurisdiction, and to execute summary punishment for offenders.
Osama: Call your mama one last time. Your time is near.
It means they get a trial under the UCMJ, not the US Criminal Code. They will have a lawyer and there are rules of evidence, but the judge and jury is typically a panel of military officers or jurists selected for their knowledge of the law and the appeals process is very limited.
Think of the Neurenberg Trials.