There are two pronunciations of this—[x] and [h]—but they are actually allophones of the same phoneme. The Vanyar use [x] in all places. The Ñoldor also use [x] for h, but pronounce it [h] at the beginnings of words. By the Third Age in Middle-earth, h is [h] in every position before a vowel.
As a consonant in its own right, y is [j]. But immediately after another consonant, y is not a consonant of its own, and palatalizes the preceding consonant or consonant cluster—see the relevant entries in this chart.
When a consonant or consonant cluster is followed by y, then the y is not a consonant in its own right and the consonant or cluster preceding it is instead palatalized.
Not all palatalized consonants are attested in official sources, but many are possible in original Neo-Quenya texts because of Quenya grammar, particularly the -ya adjective suffix. This can be seen in the word Quendya/Quenya itself: Quendë "elf" + ya adjectival suffix = Quendya or Quenya "elvish", where n in ny becomes palatalized, and the pair nd in ndy both become palatalized (as if they were ny+dy).
Note the absence of cy gy—they are forbidden, instead becoming ty dy. Likewise, the clusters ncy ngy become nty ndy among the Vanyar, or nty ny among the Ñoldor.
gy becomes this.
cy or ky become this.
Syllable stress is not phonemic in Quenya, but the language does have a well-defined syllable stress which is fairly predictable.
In words with two syllables, the first syllable is stressed.
In words with three or more syllables, the antepenultimate (third-to-last) syllable is usually stressed. However:
If the penultimate (second-to-last) syllable is either a long vowel, a diphthong, or ends with a consonant cluster (including x, but not hw or qu or a single palatalized consonant), then this syllable is stressed.
In the Quenya as studied in Gondor in the Third Age, the sequences ty dy hy (normally [c ɟ ç]) are pronounced [tʃ dʒ ʃ].
In some circumstances, dh is actually the consonant cluster d-h, pronounced as two separate letters.
Pronounced [f] normally, but is [v] before n and at the ends of words.
Short vowel. Pronounced [j] before another vowel.
In some circumstances, lh is actually the consonant cluster l-h, pronounced as two separate letters.
An older Sindarin consonant that soon becomes v. Also, in some circumstances, mh is actually the consonant cluster m-h, pronounced as two separate letters.
Normally pronounced [ŋɡ], but is [ŋ] at the end of a word.
Confusingly, this represents two sounds in First Age Sindarin. [oe] is a diphthong, and [ø] is a single vowel. The latter later becomes pronounced and written like e. Perhaps the most famous word known to be spelled with oe as [ø] is "Nirnaeth Arnoediad".
Normally pronounced [fː], but is [f] at the end of a word.
In some circumstances, rh is actually the consonant cluster r-h, pronounced as two separate letters.
Short vowel. The traditional pronunciation is [y]. By the Third Age, all varieties of [y] become pronounced [i] instead.