*All characters belong to J.K. Rowling. I'm not making any money off this.
Harry didn't even know what it was he was trying to find out. He knew better than to even attempt sneaking into Snape's personal quarters. He guessed that anything of a remotely personal or secretive nature would lie in there. Snape didn't seem the type to write a tell-all diary or leave a pensieve around for people to stumble onto.
"Lumos."
Following the glow at the end of his wand, his eyes focused on a smooth, slightly worn away grey rock on the professor's desk. He'd noticed Snape occasionally held the small rock in his hand as he looked over the students' potions. He'd occasionally leave it temporarily on a shelf, or his desk, or sometimes even on a student table when walking around the room, before absent-mindedly scooping it up again in his hand and rubbing his thumb over the smooth surface as he angrily barked orders or berated student efforts.
The rock was all Harry needed.
Ron's father, Arthur Weasly told Harry all about investigation methods used by the Ministry of Magic when Harry stayed at the Weasly home two weeks before school started.
Following Death Eater raids, the Ministry would search for natural objects the victims may have been in contact with for an extended period of time. For example, an abandoned bathtub full of water, an unfortunate torture victim's fire in a fireplace used to burn him, even the sand in a dead child's sandbox would do. The only catch was the natural object had to be primarily in contact with one person. A stone or wooden floor traveled upon by many would never work.
The investigator would place a soft, white cotton cloth near the object and recite a complex spell which would transfer the high adrenaline, often tragic experiences of the person from the natural object into the cloth. Another spell directed at the cloth would then play the experiences or memories like a movie directly on the cloth as if it were a viewing screen. Not only would the Ministry see what had happened that particular day or week, but they could see, if they wanted to, any high-adrenaline moment from the person's lifetime.
Mr. Weasley's first mistake was giving Harry an extra cloth as a souvenir. It didn't take long for Harry and his two friends to sneak into the restricted area of the library and copy down the spells they would need.
Ron hated Snape almost as much as Harry and egged him on in trying to find out what the slimy git was up to. While Hermione was convinced that Snape should be trusted, she couldn't resist the challenge of learning this complex and fascinating investigation method. Maybe, after all, she would be finally proven right about Snape.
Harry clumsily pulled out the cloth, hung it above the rock without touching it, and recited the first spell. Quickly, he stuffed the cloth in his pocket and slipped out of Snape's office. He recited the password which re-locked the door, and crept as quickly as possible back to the Gryffindor common room where Ron and Hermione were waiting anxiously.