Ousama Kassir was extradited to the United States in September 2007 from Prague, where he was jailed after his arrest in 2005 during a stopover while flying from Sweden to Lebanon.
"This case concerns a global conspiracy that takes place down here in the United States," assistant US attorney Michael Farbiarz told judge John Keenan in the US district court in Manhattan.
Kassir, 43, is charged with conspiring with others to set up a "jihad" (holy war) camp in Oregon, in the northwest United States, that would offer military weapons training for Muslims interested in fighting in Afghanistan.
Kassir declared his innocence when he was charged last year, and his lawyer on Tuesday said his client had "a big mouth," but was not a criminal.
Kassir arrived in the United States in 1999 and spent a year at an Oregon ranch, imparting religious teachings at a Seattle mosque before returning to Europe, according to the prosecution.
"You are going to see a knife that he used for training at the ranch," Farbiarz told the jury as Kassir, in a red tunic, listened through an interpreter.
"You will see the bomb making manuals and the poison making manuals," he added.
Farbiarz said next week he would call James Ujaama, a former activist from Seattle who has admitted supporting the Al-Qaeda network and is now a witness for the prosecution.
Kassir allegedly admitted before witnesses he supported Al-Qaeda and its boss Osama bin Laden.
The US government also accused Kassir of being a follower of Egyptian Muslim cleric Abu Hamza al-Masri, currently jailed in Britain for inciting to violence.
"He did it for Abu Hamza, he did it for Al-Qaeda, he did it for Jihad," Farbiarz said.
Defense lawyer Mark DeMarco denied the charges, and said his client was not a terrorist.
"He is certainly not a terrorist, he is certainly not a member of Al-Qaeda," said DeMarco.
He asked the jury for "a fair trial."
The trial is expected to last at least four weeks. Kassir could face life in prison if found guilty.
Kassir was born in Lebanon and has Swedish citizenship.