Defence lawyers are expected to argue that information used in the investigation, in which the CIA was involved, was obtained illegally through surveillance in Germany and Pakistan.
German police arrested three of the men; Fritz Gelowicz, Daniel Schneider and Adem Yilmaz, at a rented cottage in central Germany in September 2007.
Turkey arrested the fourth, Attila Selek, two months later, and extradited him to Germany.
It is alleged the defendants had collected 26 detonators and 12 drums of hydrogen peroxide, and mixed chemicals to make around 100 times the amount of explosives used in the July 2005 bombings in London.
Ralf Setton, a prosecutor at the trial, told the court on Wednesday that the defendants aimed to kill as many people as possible, saying they were moved by a "profound hatred of the USA as the greatest enemy of Islam".
The trial at Duesseldorf state court, which has been surrounded by tight security, is expected to continue until the end of August.
German media have dubbed it the country's biggest "terror trial" since members of the Red Army Faction, or Baader Meinhof gang, faced murder charges in the 1970s.
The defendants could face up to 15 years in prison.