There are six faces of the cube: F (front, toward you), B (back), U (up), D (down), L (left), and R (right). The same letters are used for turns. R is a clockwise twist of the Right face, U is a clockwise twist of the Up face. The ' shows a counterclockwise twist, for example R'. A 2 shows a 180° double twist, for example R2. For visually oriented people, we have diagrams which show how to turn a face when looking at the front of the cube.
You need to get the white cubies all together and positioned correctly with respect to each other. Orienting the white cubes is easy; getting them into the correct positions is only a little more difficult.
View from the Front (mostly)  Algorithm (viewed from the Front!) 

and then as above, or

Flip the cube over to work on the yellow corners. The goal is to get all the yellow sides facing up (correct orientation, but not necessarily correct position).
View from the Top  Algorithm (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.
 
This is the Inverse Mu (μ) pattern. Apply Sune once to get (rotated) Mu pattern. Then rotate the cube (or just the U face) so it looks like the Mu pattern above, and apply the Sune algorithm a second time.  
Checker Board pattern.
Apply Sune once, to get (rotated) Inverse Mu pattern.  
Apply Sune algorithm once to get (rotated) Inverse Mu pattern. Rotate the cube into the Inverse Mu pattern, and solve that.  
Apply Sune algorithm once to get (rotated) Mu pattern. Rotate the cube into the Mu pattern, and apply Sune algorithm again.  
Apply Sune algorithm once, to get Inverse Mu pattern. Rotate the cube into the Inverse Mu pattern, and solve that.  
Apply Sune algorithm once, to get the Mu pattern.
Apply Sune algorithm again.  
This is the Inverse Mu (μ) pattern in a different arrangement,
if you want to learn a second algorithm (Inverse Sune):

You have the whites all on bottom facing down, and the yellows all on top facing up. Count the pairs along top and bottom halves of the sides of the cube. The goal is to get eight pairs. If you were careful to Orient and Position White Corners in the first step, you will find either 4 pairs all on the bottom half of the cube, or 5 pairs with four on the bottom and one on the top half of the cube. We start with the 5 pairs because that is most common, and its algorithm can be used to solve all the rest of the combinations (including 0, 1, and 2 pairs if you did not position the white cubes correctly in the first step).
Number of Pairs  Algorithm 

5 Pairs, with the single upper pair away from you (on the B side of the cube).  
4 pairs, with the 4 pairs on the bottom half of the cube.  Apply the 5 Pairs algorithm once. You should get 5 Pairs, with the upper pair facing R. Rotate the cube so the upper pair is facing B. Apply the 5 Pairs algorithm again. 
2 Pairs, with both pairs toward B.  Apply the 5 Pairs algorithm once. You should get 5 Pairs, but with the 4 pairs on the top half and 1 pair on the bottom. Flip the cube over so the 1 pair is on the top half and facing B. Apply the 5 Pairs algorithm again. 
0 Pairs 
You can solve this with four(!) applications of the 5 Pairs algorithm, but
you can learn just one more short algorithm to solve this setup:

1 Pair, with the single pair on the upper B side of the cube.  Apply the 5 Pairs algorithm once. You should get 4 Pairs. Flip the cube over so the 4 Pairs are on the bottom half and solve as above. 