How does Jean Valjean turn his life around after his confrontation with the bishop? Use two quotations for support and commentary.

The last thing the Bishop says to Jean Valjean is

Do not forget, do not ever forget, that you have promised me to use the money to make yourself an honest man.

As we read the rest of Valjean's story, we see how the encounter with the Bishop has influenced him.
Valjean is a poor and homeless guest of the Bishop, yet he robs the holy man. Valjean even comes close to murdering the Bishop before taking the silverware.
The next morning, the Bishop is not fazed by the robbery, and when the police show up with Valjean, the Bishop easily proclaims that he gifted the silverware to the man and hands over the silver candlesticks as well. We can see the effect this has on Valjean simply from his reaction:

Jean Valjean opened his eyes wide, and stared at the venerable Bishop with an expression which no human tongue can render any account of.
...
“Is it true that I am to be released?” he said, in an almost inarticulate voice, and as though he were talking in his sleep.

Valjean does indeed turn his life around.

And as he wept a new day dawned in his spirit, a day both wonderful and terrible.

Valjean confesses his identity when another man is mistaken for him. It would have been easy to let this other man take the fall and let Javert believe he captured the ex-con. Instead, Valjean speaks up. He takes in Cosette, the illegitimate child of Fantine, the prostitute. He raises Cosette and follows her love, Marius, to the barricade, watching out for him and bringing him home. At the barricade, Valjean takes care not to kill, even sparing the life of Javert, who has been hunting him. This is significant because Valjean journeys from almost killing the innocent Bishop to freeing Javert, the man who has caused him trouble.
On his deathbed, Valjean shows us his religious influence in his new life:

"I have one," Jean Valjean replied; and he pointed upwards as though there were some other being present whom he alone could see.