A cryptogram is a quote with every letter swapped for another one, consistently, all the way through. Swap A for Q once and every A in the puzzle becomes a Q. That single rule is the whole game, and it's also the whole way in: patterns survive the swap even though the letters don't. A three-letter word is still a three-letter word. A doubled letter is still doubled. You're not breaking a code so much as reading the shape of English through a disguise.
Start with frequency, not guessing
English letters aren't used equally. E, T, A, O, I and N do most of the work, in roughly that order, while J, Q, X and Z barely show up. Count the letters in the cipher text before you touch anything else. Whatever appears most is very likely E, or close to it. That single count usually hands you your first correct guess before you've made a single deduction.
This is a starting hypothesis, not a certainty, especially on a short quote where the sample size is small. Write it in lightly and keep testing it against everything that follows.
The short words break it open
There are only two one-letter words in English: "I" and "A." Any lone cipher letter standing by itself is one of those two, and if it's followed by an apostrophe it's almost always "I" (I'M, I'VE, I'LL). The most common three-letter words are "THE" and "AND," so a repeated three-letter cluster is worth testing against both before anything else.
Punctuation gives away structure too. A sentence ending in a question mark is likely to contain WHO, WHAT, WHEN, WHERE, WHY or HOW somewhere in it. An apostrophe followed by a single letter is almost always 'S or 'T. Once you've placed even three or four letters this way, longer words start solving themselves, because most of their letters are already filled in.
Doubled letters and the Q rule
Two identical cipher letters sitting next to each other are almost certainly L, E, S, O or T doubled, roughly in that order of likelihood. And a Q, wherever it lands, is followed by U nearly every time in English. Neither of these solves a puzzle on its own, but both are free eliminations, and free eliminations compound: every letter you pin down removes candidates from every word it appears in, not just the one you were looking at.
The one guarantee you can lean on
Fair cryptograms, the kind published in newspapers and the kind on this site, never let a letter stand for itself. A never encodes to A. If you're staring at a cipher letter and trying to decide whether it might just be the plaintext letter in disguise, it can't be, and you can strike that option immediately. It's a small rule, but it prunes the search space on every single letter of the puzzle at once.
That guarantee isn't an accident. Our generator builds the cipher as what's called a derangement: a shuffle of the alphabet that gets thrown out and reshuffled if any letter lands on itself, over and over until one qualifies. About six in ten random shuffles fail that check on the first try, which is why it's a loop and not a one-shot swap.
How we built the hints
The daily cryptogram pulls from a pool of 229 quotes, all public domain, each one certified to have at least ten distinct letters before it's allowed into rotation. Fewer than that and a solver runs out of frequency signal to work with; the puzzle stops being solvable and starts being a guess.
You get three hints per puzzle, and we thought hard about which letter each one should reveal. The easy choice is to hand over whichever letter is highest-frequency, since that unlocks the most words at once. We built it backwards instead: a hint reveals the least frequent unsolved letter left in the puzzle, the one frequency counting was least likely to hand you on its own. Reveal the E and you've barely spent a hint, since the method above finds it anyway. Reveal the puzzle's lone Z or Q and you've spent it on the one letter no amount of deduction was going to surface quickly.
Run the method above against today's puzzle and it should get you most of the way before you need a single hint. Older days are in the cryptogram archive if you want more practice.