Twist the corners
The step where you have to trust the process.
Now we twist the yellow corners so yellow faces up. This is the step where you have to trust the process. Hold the cube with a twisted corner at the front right, on top. Repeat R prime, D prime, R, D, until its yellow faces up. The bottom looks broken now. Don't panic, and don't turn the whole cube. Turn only the top, to bring the next twisted corner to the front right. And repeat. When every corner is done, the bottom fixes itself.
Your turn. Twist the corners until yellow faces up on all of them. Trust the bottom to come back.
Every corner is solved, and the bottom came back.