The story
In December 1903 Arthur Conan Doyle published The Adventure of the Dancing Men. A country house in Norfolk keeps finding rows of little stick figures, chalked on a door, scribbled on paper, left on a sundial. They look like a child's game; they frighten the lady of the house badly. The detective collects every sample, notices that one figure is far commoner than the rest and decides it must be E. Some of the figures hold small flags, and he guesses that these mark the ends of words.
From there he works exactly as a codebreaker would: short words, a likely name, a likely place, until the whole alphabet falls out. He even uses the broken cipher to write a message back in the same figures. The figures on this platform are our own, but the method is his.
A real method in a story
Doyle was not the first to put frequency analysis into fiction. Edgar Allan Poe had done it in 1843 in The Gold-Bug, where a pirate's message in printer's symbols is broken by counting, and E again comes first. Both stories taught a large public that a cipher made of strange signs is no stronger than one made of letters.
Printed versions of the 1903 story contain a few slips: in some editions one figure seems to be used for two different letters, which has kept puzzle fans busy for a century.
Pictures instead of letters
Symbol alphabets are old and popular: the pigpen cipher of the freemasons (letters replaced by bits of a grid), secret alphabets in diaries, the signs schoolchildren invent. Each one feels private. Each one is still a single fixed alphabet.
How it was broken
Exactly like any other monoalphabetic substitution: count the signs, match the commonest to E, T, A, O, look for short words and repeated patterns. Flags at word ends make it easier still, because they hand the codebreaker the word lengths. A safer writer would have left the flags out, or used several figures for E, the trick Renaissance cipher secretaries had already learned.