How did Rey become a Jedi?
First lets look at Anakins and Lukes journey to become a Jedi.
Anakin trained with Obi-Wan for 10 years and still wasn't made a Jedi until the events in AOTC.
"But Anakin was not made to take such trials, so then how did he become a Jedi Knight?
Well, it was through his efforts during the first year of the Clone Wars, that proved his worth as a Jedi Knight, and also some convincing by Obi Wan.
Obi Wan, before he became a Jedi Master and had a seat on the council, requested an audience with them to discuss Anakin’s progress as a Jedi. There, he vouched for Anakin’s experience during the war, and that through his valiant efforts on the battlefield had essentially passed the Jedi Trials, and they would therefore be redundant. He came before them requesting that Anakin be made a Knight, and that there was little more that he could teach him.
The council agreed, and they arranged the knighting ceremony for Skywalker, where Obi Wan and Anakin would no longer be master and apprentice, but equals, and brothers in the Force."
Luke did not become a Jedi until ROTJ when Yoda told him that he would have to face Vader to become a Jedi.
"He received his initial training from Obi-Wan Kenobi and additional training from Yoda, but he did not become a Jedi until his final confrontation with Vader on the Death Star under construction in Return of the Jedi:
Yoda: No more training do you require. Already know you, that which you need.
Luke: Then I am a Jedi.
Yoda: No. Not yet. One thing remains. Vader. You must confront Vader. Then, only then, a Jedi will you be. And confront him you will."
Rey: In the TLJ, Luke says that she is the last Jedi. Now how and why did Rey become a Jedi with no training or explanation of anything. There is still no explanation of why she is so skilled with a laser sword and was able to fight with Kylo to defeat the red imperial guards with such grace and skill.