Final first layer corner (~8 moves)
The first corner to tackle is the one in the first layer, which will give us two full layers (and more) solved.
There are three possible scenarios, depending on the cubie in the final layer that has the first layer sticker. If you started with white, this is the only cubie in the last layer that has a white sticker.
- The sticker (e.g. white) is in the last layer. For people who already know Fridrich a bit, we solve this case using the A permutation - we pretend the face with the unsolved corner is our last layer.
For this algorithm, make sure the first layer is now in the back, and the unsolved corner (first layer) is on the right. The cubie that is in the last layer should now face FLU. The cubie will move diagonally across the face. Now perform this algorithm
moves will appear here
- When the sticker is on one side, you can perform the inverse of this same algorithm. Keep the sticker and the empty slot on the right, and the first layer in the back, perform
moves will appear here
- Same as #2, but with the sticker and empty slot on the left:
moves will appear here
There are several other algorithms you could use, mostly from the Fridrich OLL series. See what is useful and adapt yourself to it.