They were contained in a publication called Inspire, described as an al Qaeda magazine.
The High Court in Glasgow heard that broken Christmas tree lights like those talked about in the instructions were also found in Taimour Abdulwahab's house in Luton.
Abdulwahab died in the explosion on December 2010 in the Bryggargatan area of Stockholm.
Nasserdine Menni is on trial charged with conspiring with Abdulwahab and others to further terrorist aims, which included the use of explosive devices in the commission of an act of terrorism directed against members of the Swedish public, with intent to murder them.
Cross-examined yesterday, Abdulwahab's wife Mona Thwany, 29, was asked whether she had heard of Inspire. She said she read that it was an al Qaeda magazine.
William Taylor, QC, defending Menni, asked: "Amongst other things it gives you instructions on how to build a bomb in your mother's kitchen. Why could it be on a computer in your house?"
She said she did not know and went on to say that the computer was used by a lot of people.
Asked whether her husband could have downloaded it, she said that she did not know.
Menni is also charged with transferring money to or for the use of Abdulwahab, in the knowledge it would be used for the purposes of terrorism. It is alleged he conspired with various people from addresses in Glasgow, Luton, Bedford, Syria, Iraq and Sweden.
He denies all charges.