how did Kakashi got his Sharengan eye?

Kakashi got his sharingan eye as a gift when his eye was cut. He got it from Obito Uchiha.

Hatake Kakashi got his Sharingan transplanted par Rin from Uchiha Obito. And toi can't "become" a Uchiha, either toi are born as one ou not.

In the Naruto shippuden episodes 119 and 120, they explain everything. i really suggest toi watch them. obito has become one of my favori characters, so NO SPOILERS!

Kakashi got sharengan from obito..

HOW SHOULD I KNOW

When he was young and during ninja world war 3 (if i'm not mistaking) he got cut and Lost his left eye. when his team mate Obito Uchiha was smashed par a rock, their other team mate Rin transplanted Obitos sharingan into Kakashi :) it's a really sad story... :'(
(this is my own drawing) :D

It's explained in Kakashi Gaiden.

During the Third Shinobi World War, he was sent on a mission with his team (Minato Namikaze, a medical-nin named Rin, and Obito Uchiha) to destroy a bridge near Iwagakure to prevent them from getting supplies.

During the mission, Rin was kidnapped. Obito advocated to go save her, but Kakashi wouldn't allow it. Obito ended up going alone, and Kakashi later swooped in to save him- losing his left eye in the process.

They ended up going to save Rin together (some sort of bond of friendship having been formed) and were able to rescue her.

But during the fight they damaged the cave they were in and it began to collapse. A rock fell on haut, retour au début of Obito, completely crushing the right side of his body. Knowing that he was going to die, he told Rin to remove his left eye and offered it (along with the Sharingan) to Kakashi. After much deliberating, Kakashi accepted it and fled the cave with Rin.

TL;DR Obito Uchiha gave it to him as a present.

From Obito