CFOP step 3: 2-look OLL, make the top yellow

OLL means orienting the last layer: turning every top piece so its yellow faces up. Full OLL does it in one algorithm, but has 57 cases. 2-look OLL splits it in two:

Make the yellow cross (the edges).
Make the whole top yellow (the corners).

That's 2 algorithms for the first look and 7 for the second. You already know some of them from the beginner method.

R U R' U R U2 R'

Sune: one of the seven corner cases

First look: the yellow cross

Look at the top face and ignore the corners. You'll see a line, an L, a dot or a cross already.

Line: hold it left to right

The beginner algorithm.

F R U R' U' F'

Line (left to right): F R U R' U' F'

L: hold it at the back-left

The beginner method needed the line algorithm twice here. This one goes straight to the cross. It's the line algorithm with R and U swapped in the middle.

F U R U' R' F'

L at the back-left: F U R U' R' F'

Dot: both

Do the line algorithm, turn the top twice, then do the L algorithm.

F R U R' U' F' U2 F U R U' R' F'

Dot: F R U R' U' F', U2, F U R U' R' F'

Second look: the corners

Now the cross is yellow. Count the corners with yellow on top, then look at where the other corners' yellow stickers point. Turn the top until the case looks like the picture, then do the algorithm.

Case	Corners up	How to hold it
Sune	1	Yellow corner at the front-left; the front-right corner's yellow faces you
Antisune	1	Yellow corner at the back-right; the front-left corner's yellow faces you
H	0	Two yellows face left and two face right
Pi	0	Two yellows face left; the other two face front and back
Headlights	2	Yellow corners at the back; the two front yellows face you
T	2	Yellow corners on the right; the other two face front and back
Bowtie	2	Yellow corners at the front-left and back-right; the front-right yellow faces you

One corner up: Sune and Antisune

Sune is the algorithm from the beginner method's yellow face step. Antisune is Sune played backwards.

R U R' U R U2 R'

Sune: R U R' U R U2 R'

R U2 R' U' R U' R'

Antisune: R U2 R' U' R U' R'

No corners up: H and Pi

R U R' U R U' R' U R U2 R'

H: R U R' U R U' R' U R U2 R'

R U2 R2 U' R2 U' R2 U2 R

Pi: R U2 R2 U' R2 U' R2 U2 R

Two corners up: Headlights, T and Bowtie

Headlights uses D moves: the bottom turns away and comes back, so the first two layers end up solved again.

R2 D R' U2 R D' R' U2 R'

Headlights: R2 D R' U2 R D' R' U2 R'

T and Bowtie use r, the right two layers together.

r U R' U' r' F R F'

T: r U R' U' r' F R F'

F' r U R' U' r' F R

Bowtie: F' r U R' U' r' F R

Which to learn first

The two edge algorithms. Then the first look never takes more than two algorithms.
Sune and Antisune. You know Sune already, and Antisune is Sune backwards.
The rest, one or two a week. Until you know a case, finish the yellow face the beginner way, with R' D' R D on each corner.

Common mistakes

Reading the corners before the cross is done. The corner cases only mean anything once the edges are yellow.
Holding the case at the wrong angle. Each algorithm works from one angle only. Turn the top until it matches the table.
Mixing up r and R. r is lower case: the middle slice turns too.