How Kakashi Got His Mongekyou Sharingan (INSIDE)!
Please read it Fully!!!!!!
This is what i think:
Kakashi knowing that the uchiha clan was annihilated went to the uchiha place where the book of secrets is. It is said that u need a sharingan to be able to read it, and with kakashi's sharingan he could have read about the mongekyou sharingan. He might have done this because when itachi and kisame came to the village, itachi done Tsukoyomi on kakashi. Kakashi wanting a strong sharingan like itachi could have went to the uchiha's secret place where the book lies untouched.
Kakashi read about the Mongekyou sharingan, its powers and how you go blind. He also read the part where it said in order to get a mongekyou sharingan, you have to kill the person closest to you. But Kakashi didn't have anyone close to him, he always kept his distance because of what happened to Rin and Obito.
Because Kakashi is a smart guy who looks at things from a different perspective/angle and he's good with his analyzing skills, he could have found a different way to get the Mongekyou.
Later Kakashi had another encounter with itachi during a mission. Kakashi said "Itachi, how bad has your eyesight become?" to itachi. Itachi was shocked. Kakashi knew this because he read the Uchiha's book with the secrets.
Kakashi obtaining the mongekyou sharingan and knowing that you'll become blind is the evidence of Kakashi going to the uchiha's secret room.
Edit: Another way is kakashi could have done a shadow clone, then the shadow clone could have put Kakashi under genjutsu, so kakashi could feel how devastating it was for obito n Rin to die.