A syllable is one beat of a word, built around a single vowel sound. Count vowel sounds, not vowel letters: “queue” has four vowel letters and one syllable. In every English word of more than one syllable, exactly one syllable is stressed — said louder, longer and on a higher pitch — and the others reduce. To find it, say the word as a question: your pitch rises on the stressed syllable.
A syllable is a vowel sound with things attached
Every syllable has exactly one vowel sound at its centre. Consonants before it are the onset, consonants after it are the coda, and either can be empty. That is the whole structure: “a” is a syllable with no onset and no coda, “strengths” is one syllable with a three-consonant onset and a four-consonant coda.
This is why counting letters fails. “Queue” has four vowel letters and one vowel sound. “Rhythm” has one vowel letter and two vowel sounds. The question is never how the word is spelled; it is how many times your jaw opens.
Across the 83,117 single words in this dictionary, 6,810 are one syllable, 23,424 are two and 23,668 are three — three-syllable words are the largest group, and the longest entries run to 13 syllables.
Where the break falls: the rule that decides
Given a run of consonants between two vowels, English has to decide which syllable they belong to. The deciding factor is the vowel in front of them.