The Z sound /z/ is usually made by any of these combinations: z-, -z-, -zz-, -zz, -ze, -se, -s-, -s, -ss-, exh-, x-, -x- and -es in English words1. (The hyphen shows where in a word the spelling pattern is used, beginning z-, middle -z-....) A single Z in an English word is normally found at the beginning of the word (zero, zebra and zest) or in the middle after a vowel (horizon, size, and freeze). A Z at the end of a word is commonly doubled. (buzz, jazz, fuzz and fizz)
There are some exceptions. The few common English words that end with a single letter Z are usually of German origin, such as Hertz, quartz and waltz; where it makes a /ts/ sound. A final letter Z also appears in foreign place names. (Examples include: Polish: Bydgoszcz, Portuguese: Cruz, Hebrew: kibbutz, Persia: Shiraz, Arabic: Suez) In words of Italian origin ZZ is pronounced /ts/ as in pizza, piazza and mezzo. In more common English words ZZ is pronounced /z/, as in buzz, puzzle and fuzzy.
In Old English, Z was only used for foreign words. Over the years, older words with a /z/ pronunciation had their spelling changed to a Z instead of an S. Many words ending with -se are pronounced /z/ or /s/. Most words ending with a consonant + se use /s/. Most words that end with a vowel + se are pronounced with /z/. For this reason, the American dictionary writer, Noah Webster changed the British English vowel + -se ending into a new American -ze spelling. For example: apologise/apologize, organise/organize; realise/realize.
Some otherwise identical words used /s/ or /z/ pronunciations to show that they were different words. The words use/use as a noun has an /s/ and as a verb has a /z/, the same pattern applies to close/close with /s/ for the adjective and with /z/ for the verb. Similarly the word prize was changed from the original (Old French) pris to avoid confusion with the word price.
Z is the least often used letter in written English. It is a little more commonly used in American English than in British English, but only because of the word endings -ize vs. -ise and -ization vs -isation, thanks to Webster’s spelling reforms. The Z sound in English is spelled many ways, but tends to fit within regular patterns.