VisualCubing
The first time someone tells you "turn the R," the natural thing is to turn whichever face is closest to your right hand. And you're wrong. Not because you're clumsy, but because nobody explained the rule before giving you the order — and once you know that rule, you never forget it.
They're not colors, they're positions
The first thing to let go of is the idea that R is "the red face" or U is "the yellow face." No. It doesn't matter what color scheme your cube has: R is whichever face is on your right at this exact moment, F is the one facing you, U is the top one. There are six letters — U, D, F, B, R, L, for up, down, front, back, right and left — and all six are defined relative to you, not to the cube. That's why, when you rotate the whole cube to look at it from another side, the letters don't move: you move, and R is still whichever face is on your right.
The apostrophe isn't decoration
A single letter, like R, means turning that face a quarter turn clockwise, looking at the face head-on. The same letter with an apostrophe, R', is exactly the opposite turn: a quarter turn the other way. It's not a footnote or a nuance for experts — it's half the language. A formula that mixes up R and R' doesn't fail a little, it fails completely.
And sometimes there's a 2
R2 doesn't mean "turn R twice in a row" as two separate moves: it's a double turn, half a rotation done in one go. You end up in the same place you'd reach by turning R twice, but it's written and thought of as a single move. With that, you've got all three pieces: the letter says which face, the apostrophe says which direction, the 2 says how much.
Everything else is a variation on the same trick
If your cube has more than three layers per side — a 4×4, a 5×5 — you'll run into lowercase letters or a w tacked onto the letter, like Rw. It's the same thing as always, just moving two layers at once instead of one. And if you ever get into blindfolded solving, M, E and S will show up for the middle slices. None of these variants change the base rule: it's still a letter, a direction and an amount.
You don't need to memorize any of this by reading it
This clicks a lot faster by touching it than by reading about it. That's why the Notation page puts a real 3D cube in front of you: press R, watch it turn; press R', watch it undo what you just did. Two minutes there beat rereading this article three times.
And if you ever run into a Pyraminx or a Skewb, don't assume the notation is the same: there, the letters name vertices, not faces, because those are what turn. Worth a look even out of pure curiosity — it clicks in about the same couple of minutes.