There is an orthographic rule:
- a, e, o are strong vowels, i, u are weak vowels. y is like i.
- There can be only one strong vowel in a syllable, they never combine into a diphthong. ca-os, le-ón, le-er
- When a strong and a weak vowel are next to each other (or separated by h) they form a diphthong. Eu-ro-pa, hia-to, rei-na
- There are cases when a strong vowel is next to two weak vowels. In that case, they also form a diphthong. Pa-ra-guay, U-ru-guay
- Finally, iu and ui are also diphthongs. The i is considered the strong vowel of the pair. Luis, viuda, Suiza
- But when a weak vowel is in its own syllable, and the stress of the word falls on it, it gets an acute accent and the diphthong is broken. ca-í-do, sa-ú-co, rí-e
But these are orthographic rules. They consider that a diphthong is any combination of letters that follow that rules, regardless of actual pronunciation. For example, people say cli-en-te but dien-te, but you wouldn't know that just by reading the words. Before, you could put an accent on the stressed syllable of some words, to show the lack of diphthong: pié (I tweeted) vs. pie (foot), enduído vs. ruido, but the new rules don't allow that.
So, to wrap it up: follow the orthographic rules and you'll know when there is a diphthong, but there'll be some false positives.