How does Vegeta become a Super Saiyan Blue? Vegeta becomes a Super Saiyan God Super Saiyan (Super Saiyan Blue) in the movie Resurrection F. How did he become a Super Saiyan God? 

Was the ritual performed on him before the Resurrection F event or did he use his own power to become a God? (That's what he tells on one of the Dragon Ball Super episodes)
The Wikia page states that:


  Super Saiyan God Super Saiyan, also known as Super Saiyan Blue, is the result of a Saiyan transforming into a Super Saiyan after absorbing and retaining the power of Super Saiyan God and training.


That is, that to achieve SSGSS, one must achieve and master SSG first.

However, as it wasn't done before Vegeta went off to train under Whis, the only options left are that either he performed the ritual on that planet, or his training with Whis helped him do so. The SSG form is just another Saiyan transformation, the only thing being different is that instead of normal Ki, there is divine Ki flowing through your body and you can even perceive it now. As a result, you can even absorb energy attacks. As Vegeta said that he mastered the SSG form, I would believe it and would further add that by mastering the form he said that he mastered the perception and usage of the divine Ki, thus making it flow through his body evenly and unlocking the SSGSS form.

There is reference to this in the anime when he senses the return of Whis (watch here), and later the oracle fish comments that he's finally able to sense divine Ki. Goku even states that Vegeta's Ki had changed a lot during the six months he had spent training under Whis (watch here). 

It's similar to that incident when Goku and Gohan had unlocked the Full Power Super Saiyan transformation after training in the hyperbolic time chamber in the cell saga. The FPSSJ transformation was the mastering of SSJ1 and making it the base form, thus reducing the strain on the body and making it easier to raise power levels. What they managed to do can be thought of controlling the SSJ1 Ki and making it flow evenly through their bodies, thus mastering the form. 

The training both Goku and Vegeta are undergoing, which deals with raising power levels, a manifestation of Ki, without letting it leak, or, in other words, letting the opponent know, making each part of the body capable of independent action and also the perception and mastery of divine Ki, thus mastering SSG, SBG (Saiyan Beyond God) and SSB transformation.