This page lives at http://www.ekrohn.com/cubing/cornersortega.html. It is based on http://rubikscube.info/ortega.php.
See notation.html for diagrams of the different moves.Aim for 6 moves or less. Customarily this is the white center and corners.
Flip cube over. Customarily this puts the yellow center on top. Now orient the four yellow corners.
View from the Top  Suneonly Algorithms (viewed from the Front!)  More Algorithms (viewed from the Front!) 

Learn this pattern (called Mu, or μ) and the algorithm (called
"Sune") to solve it and
you can solve all the yellow face orientations that can occur.
The Sune leaves the corner by your left thumb unchanged;
it twists the other three corners Clockwise (CW).
The final U2 can often be skipped.
R U R' U R U2 R' [U2]  
This is the Inverse Mu (or μ) pattern.
The wrong corners need a CCW twist, or two CW twists.
The final U2 can often be skipped.
Apply two Sune algorithms.

The AntiSune algorithm:
L' U' L U' L' U2 L [U2] The AntiSune leaves the corner by your right thumb unchanged; it twists the other three corners CounterClockwise (CCW).  
This is the L (F) pattern.
(On the 2x2 cube this was called the Checker Board pattern.
We could also call it the "Diagonal" or "Backslash" pattern.)
Apply Sune once, to get (rotated) Inverse Mu pattern, then solve that pattern. 
Or learn one of these two algorithms:
 
This is the Bug Eye or T pattern.
First do U' to set up, then apply Sune algorithm once to get (rotated) Inverse Mu pattern. Rotate the cube into the Inverse Mu pattern, and solve that.  The shorter Bug Eye algorithm: (R U R' U') F' U' F  
Pi pattern.
First do U to set up, then apply Sune algorithm once to get (rotated) Inverse Mu pattern. Rotate the cube into the Inverse Mu pattern, and solve that. 
Or learn this algorithm for the Pi pattern:
y F (R U R' U') (R U R' U') F'.
This is shorter: R U R2 F' R'2 U R', but it swaps the FBR and FBL corners, making the next step longer.  
U or Headlight pattern.
First do U2 to set up, then apply Sune algorithm once to get (rotated) Inverse Mu pattern. Rotate the cube into the Inverse Mu pattern, and solve that. 
Shorter algorithm for U pattern:
R' F' U' F U R
Or: y' F (R U R' U') F'  
H pattern.
First do U to set up, then apply Sune algorithm once, to get the Mu pattern. Apply Sune algorithm again. 
R2 U2 R' U2 R2
This may mess up the top row pairs, but they would rarely be correctly paired
at this point.
Or F (R U R' U') (R U R' U') (R U R' U') F' 
Have X's on top and bottom, want X's on all sides. Count the pairs along the top and bottom edges of sides. (For example, hold the cube with the Yellow center and corners on the U face. You need to count sidebyside pairs of same colors of Blue, Green, Red, and Orange.)
If you solved the white corners with the pairs matched, you will have either the 5pair or, less commonly, the 4pair pattern. If you only oriented the white corners, but did not correctly position them, you could have any of the following patterns.
Number of pairs  Short algorithm  5pair only algorithm 

0 pair  R2 F2 R2  While you can do four 5pair algorithms to solve the side, it really is much easier to just learn the short 0pair algorithm! 
1 pair 
on DL: R2 U' R2 U R2 U' R2 U R2
on DB: R U' F U2 F' U R' on UB: R' U R' B2 R U' R 
Turn the cube so the one pair is at UB: do the 5pair algorithm to get 2
pairs. Then solve for two pairs.
Or, put the one pair on UR, do the short 0pair algorithm to get 5 pairs, then do the 5pair algorithm once. 
2 pair  pairs on B: R2 U F2 U2 R2 U R2  Do one 5pair algorithm. Flip the cube top to bottom, then do another 5pair algorithm. 
4 pair 
pairs on D: [F2 U' R U' R' U] [F2 U R U R']
or 2 pair twice, or 1 pair twice  Four pairs on D: do one 5pair algorithm. Rotate the cube with y', then do another 5pair algorithm. 
5 pair 
The one pair on UB:
R U' R F2 R' U R F2 R2 or 2 pair twice, or 1 pair twice 
At this point, both the U and D faces will have their corners solved, and you need to solve the edges. The "keyhole" will be a slot (edge) on the U face that you want to fill. The "target" will be the edge piece that needs to be moved into the keyhole. If the U color is Yellow, position the keyhole at UL and the "target" edge piece you need to move into that slot on the H slice with its Yellow color facing your right hand. If the target edge is at RF, then L H L'. If the target edge is at RB, then L' H' L. Once you see the pattern, you'll also know how to move a target piece into a keyhole in the D face; until then, just flip the cube upside down to solve the White edges.
Be attentive! As you move the target piece into the UL edge position, you will bump out the piece in the DL edge position. You either need to rotate the D face so that an "expendible" piece is in DL, or arrange for the UL edge piece to solve the DL edge at the same time that you solve the UL edge.
You want to end up with the entire U and D faces (e.g., White and Yellow) solved, except for one final keyhole.
Position "keyhole" at UR, and target at FL with target L color matching U face.
R' H R2 H R'
Another possibility is to solve the last keyhole on the U face and the last keyhole on the D face at the same time. It requires a little more planning of your moves, but it is not difficult.
Rotate cube so the two finished sides are L and R. Only the four middle edge pieces need to be solved.
Cycle 3 edges down:  M' U2 M U2  Cycles BU to FU to FD. BD does not move. 
Swap FU/BU and FD/BD:  M'2 U2 M'2 U2 
Swap FU/BD and FD/BU (cross corner pattern):  H2 M' H2 M' 
Flip FU and flip BU:  [M' U M' U M' U2] [M U M U M U2] 
If diagonally opposite, setup with F2,
then finish with another F2. 
Your cube should now be solved!