Step 4 · PLL (Permute the Last Layer)

The top is all yellow. Now move the top pieces to their correct spots. Full PLL has 21 cases. 2-look PLL does it in two steps with 6 algorithms: corners first, then edges.

2-look PLL Step 1: corners Step 2: edges All 21 PLLs Recognition & AUF Finger tricks

Arrows show where each piece needs to go. A move in parentheses after an algorithm, like (U'), is the final turn of the top needed for the case as drawn. That last turn is called the AUF (adjust U face).

2-look PLL (6 algorithms)

Look 1 · Solve the corners

Look at the two corner stickers on each side. When the two corner stickers on one side are the same color, that's called headlights:

Headlights on one side → two neighboring corners need to swap. Put the headlights on the left and do the adjacent swap (it's the T perm).
No headlights anywhere (every side's corners are different) → two diagonal corners need to swap (it's the Y perm).
Headlights on all four sides → corners are already solved. Go to look 2.

In the pictures, the edges are grayed out because they don't matter yet.

The diagonal swap is two parts. Watch the front pair: F, put the pair in, U', take it back out, F'. Then: take the front-right pair out, bring it back, and put it in a different way. The adjacent swap uses the same pieces in a different order, and the second half starts with the same "four moves".

Look 2 · Solve the edges

One edge already solved (a full solid bar): hold it at the back. Ua or Ub, depending on which way the other three need to cycle. J Perm's way to tell: find the side piece that needs to go to the opposite side. If it's on the right, it's Ua. If it's on the left, it's Ub.
No edge solved: if opposite edges swap, it's H. If neighboring edges swap, it's Z (put the swapping edges on the front and right).

Lazy option for Ub: do Ua from the left side. It's faster in the long run to learn both with the right hand. For M moves: M2 is ring finger then middle finger flicking from the back. M' goes up.

All 21 PLLs

Learn full PLL alongside advanced F2L, going back and forth (J Perm's roadmap). You already know 6 of these from 2-look PLL: Ua, Ub, H, Z, T and Y. "A lot of them are very similar to each other."

Recognition & AUF

Recognize from any angle, don't rotate. At first it helps to line up blocks with the centers and rotate the cube so the case is in a familiar spot. Eventually, pretend the first two layers aren't there. Recognize the case from the top-layer patterns alone (headlights, bars, blocks). Start the algorithm from wherever your hands are and fix the alignment at the end with one U turn.
Predict the AUF during the algorithm. Don't finish the PLL and then stop to figure out the last turn. That can waste half a second on a single move. Before you start, pick something to track. In many PLLs a block stays where it is, so you know which way to turn at the end. In some (like the R perms) the block moves, so remember a color instead: "green belongs at the back, so it'll be U2 afterwards".
Use any algorithm from someone fast at first. Don't hunt for "your" best algorithms until you know more finger tricks. Early on it's hard to judge what's actually good. J Perm's example: there's a J perm alg that's easier for beginners, but with practice the standard one is much better.

Finger tricks for PLLs

T perm: do the F with your left thumb pushing up, and the F' at the end with your right thumb. No regrip needed.
A perms: tilt down (x) and do the D2s as double flicks: ring finger then pinky (or pinky then ring).
E perm: the D moves go back and forth with your ring finger. When your right thumb is on the bottom, push D with the left ring finger instead of regripping.
U perms: there are R/U versions (in 2-look above) and M/U versions (in the full list). If you're not used to M moves, the R/U ones are fine.
H perm: M2 U M2 U2 M2 U M2. Practice the M2 flick (ring + middle) and the U2 double flick (index + middle).

Sources: Easy 2-Look PLL Tutorial (algorithms from the description), [New] All 21 PLL Algorithms & Finger Tricks (groups from its chapters; that video had no subtitles, so the full algorithms are J Perm's standard set from jperm.net), and Top 10 Most Common Speed Cubing Mistakes. All 21 were checked in a simulator. Each keeps F2L and OLL intact, and together they cover all 21 distinct PLL cases.