regional.es.distincion
Distinción: the /θ/ of z and ce/ci in Peninsular Spanish
Central and northern Spain pronounce z and c-before-e/i as /θ/, the th of think, keeping them apart from s. It is not a lisp and not a royal affectation, and it is not even universal in Spain: Andalusia and the Canaries largely do not distinguish.
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Explanation
The rule is purely orthographic and has no exceptions: z in any position, and c before e or i, are /θ/; s is /s/; and c before a, o or u is /k/. So zapato, zumo, azul, paz, cielo, cinco, cerveza all carry /θ/, while sopa, casa, mismo carry /s/, and casa, cosa, cuna open with /k/. Because Spanish spelling avoids ze/zi (writing ce/ci instead), the two letters divide the same sound between them — which is why zapato and cielo rhyme in their consonant despite looking unrelated.
The sound is interdental: the tongue tip touches the upper teeth, exactly as in English think or thumb, and it is unvoiced. Two errors are common in learners. Overshooting it into something closer to /s/ collapses the distinction you were trying to make; extending it to the letter s produces ceceo, a different and geographically restricted phenomenon that will sound Andalusian rather than Castilian. Keep s firmly as /s/ — that is precisely what makes a speaker a distinguidor rather than a ceceante.
Two things to keep in proportion. First, distinción is not the Spanish norm but a Spanish one: it covers central and northern Spain, while western Andalusia has ceceo, eastern Andalusia and the Canaries have seseo, and all of Latin America has seseo. Calling it "correct Castilian" is a social judgement, not a linguistic one. Second, the story that Spaniards started distinguishing to imitate a lisping king is folklore with no historical basis: the split is a regular sixteenth-century sound change. For a learner, the practical upside is real though — if you distinguish, you also hear the c/z/s spelling, which speakers who sesean have to memorise.
Examples
Five beers and a juice, please.
Region: ES (centre/north)
The house is near the square.
Region: ES (centre/north)
I'm going to Zaragoza in December.
Region: ES (centre/north)
Don't confuse house with hunt.
Region: ES (centre/north)