The nominative singular is the basic, uninflected form of the noun; it has no special ending. The typical function of a nominative noun is to be the subject of a verb, like lómë "night" or aurë "day" in the cries heard before and during the Nirnaeth Arnoediad: Auta i lómë! "The night is passing!" Aurë entuluva! "Day shall come again!" (Silmarillion chapter 20).
Quenya as spoken in Valinor had an accusative that was formed by lengthening the final vowel of the noun: cirya "ship" (nominative), ciryá "ship" (accusative). Nouns ending in a consonant presumably had no distinct accusative. In the plural, even nouns ending in a vowel had the ending i, e.g. ciryai "ships" (nominative ciryar). The function of the accusative was primarily to mark that the noun was the object of a verb; we have no examples but may construct one like haryan ciryá, "I have a ship" (haryan ciryai "I have [several] ships"). But in Middle-earth, the distinct accusative case disappeared from the speech of the Noldor (such things happen when you are busy fighting Orcs, Balrogs, and Dragons), and the nominative took over its former functions. So from now on it was OK to say haryan cirya, haryan ciryar. Modern writers seem never to use the distinct accusative.
The genitive has the ending -o, generally corresponding to the English ending 's, though a Quenya genitive is often better rendered by an of-construction in English. One example from Namárië is Vardo tellumar "Varda's domes" or "(the) domes of Varda". Notice that the ending -o displaces final -a, hence Vardo, not Vardao - but most other vowels (it seems) are not displaced: In MR:329 we find Eruo for "the One's, Eru's". (If the noun ends in -o already, the ending becomes "invisible"; normally the context will indicate that the noun is a genitive and not a nominative. An attested example is Indis i Ciryamo "the mariner's wife"; cf. ciryamo "mariner".) Infrequently the genitive carries the meaning "from", cf. Oiolossëo "from Mount Everwhite, from Oiolossë" in Namárië - but this is usually expressed by means of the ablative case instead (see below). The plural genitive ending is -on, that may be observed in the title Silmarillion, "of the Silmarils", the complete phrase being Quenta Silmarillion, "(the) Story of (the) Silmarils". An example from Namárië is rámar aldaron, "wings of trees", a poetic circumlocution for leaves. The ending -on is added, not to the simplest form of the noun, but to the nominative plural. So though "tree" is alda, "of trees" is not **aldon, but aldaron because the nominative plural "trees" is aldar. Cf. also Silmaril, plural Silmarilli, genitive Silmarillion. (The doubling of the final l of Silmaril before an ending is an example of stem variation; some stems change slightly when an ending is added, often reflecting an older form of the noun.)
Then there is the possessive, by some called the "associative" or "adjectival case"; Tolkien himself speaks of it as a "possessive-adjectival...genitive" in WJ:369. This case has the ending -va (-wa on nouns ending in a consonant). Its general function is like the English genitive, to express ownership: Mindon Eldaliéva "Tower of the Eldalië". The function of the possessive was long poorly understood. In Namárië it occurs in the phrase yuldar...miruvóreva, "draughts...of mead". This one example, that for more than twenty years was the only one we had, made many conclude that the function of this case was to show what something is composed of - indeed the case itself was called "compositive". Luckily, The War of the Jewels p. 368-369 finally gave us Tolkien's own explanation of the more normal functions of this case, and how it differs from the genitive. The possessive can, as already stated, denote possession or ownership. Tolkien gives the example róma Oroméva, "Oromë's horn", used of a horn that belonged/belongs to Oromë at the time that is being narrated (past or present). Genitive róma Oromëo would also translate as "Oromë's horn", but properly it would mean "a horn coming from Oromë", implying that the horn had left Oromë's possession at the time that is being narrated. However, the genitive intruded on the functions of the possessive in later ages. Cf. genitive Vardo tellumar, not possessive *tellumar Vardava, for "Varda's domes" in Namárië (if the genitive does not imply that the domes originated with Varda rather than that she owns them).
The dative has the ending -n. This ending generally translates as the preposition "for" or "to"; the dative pronoun nin "for me" (from ni "I") is found in Namárië: Sí man i yulma nin enquantuva? "Who now will refill the cup for me?" Often the dative corresponds to an indirect object in English: *I nís antanë i hínan anna, "the woman gave the child a gift" (gave a gift to the child).
The locative has the ending -ssë, that carries the meaning "on" or "in". In the Tengwar version of Namárië that is found in RGEO, the poem has the superscript Altariello Nainië Lóriendessë, "Galadriel's Lament in Lóriendë (Lórien)". In the plural, this ending has the form -ssen, seen in the word mahalmassen "on thrones" in UT:305 cf. 317 (mahalma "throne"). This ending also occurs on the relative pronoun ya in Namárië: yassen "wherein, in which" (Vardo tellumar...yassen tintilar i eleni, *"Varda's domes...in which the stars tremble"). Refering back to a singular word, "in which" would presumably be yassë. The use of case endings rather than prepositions to express "in, from, to, with" (cf. the next paragraphs) is a characteristic feature of Quenya grammar.
The ablative has the ending -llo, that carries the meaning "from" or "out of". An example from Namárië is sindanóriello, "out of a grey country" (sinda-nórie-llo: "grey-country-from"). There is also the word Rómello, *"from (the) East", contraction of *Rómenello (Rómen "[the] East"). Cf. also the word Ondolindello "from Ondolindë (Gondolin)" in J. R. R. Tolkien - Artist and Illustrator p. 193.
The allative has the ending -nna, meaning "to", "into" or "upon". Both the ablative and the allative are exemplified in the words spoken by Elendil when he came to Middle-earth after the Downfall of Númenor, repeated by Aragorn at his coronation (LotR3/VI ch. 5): Et Eärello Endorenna utúlien. "Out of [lit. out from] the Great Sea to Middle-earth I am come" (Endor(e)-nna "Middle-earth-to"). The allative may also carry the meaning "upon"; cf. i falmalinnar "upon the foaming waves" in Namárië (-linnar being the ending for partitive plural allative; see below).
The instrumental case has the ending -nen and marks the instrument with which something is done, or simply the reason why something happens. Examples from Namárië are laurië lantar lassi súrinen,"like gold fall [the] leaves in [or by] the wind", i eleni [tintilar] airetári-lírinen, "the stars tremble in her song, holy and queenly", literally *"the stars tremble by holyqueen-song". An example of a more typical "instrumental" instrumental is provided by the sentence i carir quettar ómainen, "those who form words with voices" (WJ:391), ómainen being the plural instrumental of óma "voice".
Respective (?): This is what some have called a case that is listed in a letter Tolkien sent to Dick Plotz in the second half of the sixties (the so-called Plotz Letter is indeed our main source of information about the Quenya cases). The ending is -s (plural -is), but Tolkien did not identify this case by any name, nor have we ever seen it used in a text. Its function is therefore wholly unknown; it has indeed been called the Mystery Case. Some writers have used it simply as an alternative locative ending. They have had no nightly visits by Tolkien afterwards, so perhaps this is acceptable to him.
If case endings are added to a noun ending in a consonant, an e is often inserted between the noun and the ending to prevent a difficult cluster from arising: Elendil with the allative ending -nna "to" becomes Elendilenna "to Elendil" (PM:401), not **Elendilnna. However, if the noun is plural, an i is inserted between the noun and the ending: elenillor "from (the) stars" (elen "star") (MC:222).
The Quenya numbers: The numbers are singular, plural, partitive plural and dual. The singular and plural need no explanation. The function of the partitive plural (so called by Tolkien in WJ:388) as opposed to the normal plural is not fully understood, but it seems that it denotes some out of a larger group. Combined with the definite article i, it may simply denote "many": The element li in the phrase i falmalinnar "upon the foaming waves" in Namárië was translated "many" by Tolkien in his interlinear translation in RGEO:66-67. Since -li is the ending for partitive plural, it was long called "multiple plural"; indeed it was thought that it simply meant "many" of the thing in question, while the normal plural only meant "several". This may be correct in some cases, but it cannot be the whole story. The dual is used with reference to a natural pair, like two hands belonging to one person (cf. the word máryat "her hands" in Namárië, -t being a dual ending, literally "her pair of hands").
The nominative plural is formed with one of two endings. The ending -r is used if the noun ends in any vowel except -ë; well-known examples are Vala pl. Valar, Elda pl. Eldar, Ainu pl. Ainur. If the noun ends in a consonant or in -ë, the plural ending is -i, and it displaces the final -ë: Atan pl. Atani, Quendë pl. Quendi. (But if the noun ends in -ië, it forms its plural in -r to avoid one ifollowing another: tië "path", tier "paths" - not **tii.) In the other cases, the plural ending is either -r or -n; for instance, the allative ending -nna has a plural form -nnar, the locative ending -ssë becomes -ssen, and ablative -llo can form its plural both in -llon and -llor. In the dative, instrumental and "respective", the plural is indicated by the element i, inserted between the stem of the noun and the same case ending as in the singular. (See the full list of endings below.)
The partitive plural has the ending -li, presumably *-eli on a noun ending in a consonant, but a contraction or an assimilated form may also be used (for instance, the partitive plural of casar "dwarf" is casalli, for *casarli). The endings for other cases are simply added following the ending -li, e.g. ciryali "some ships" > allative ciryalinna (or ciryalinnar) "to some ships". Note, however, that the vowel of -li is lengthened before the endings -va and -nen for possessive and instrumental, respectively: -líva, -línen.
Like the nominative plural, the nominative dual is formed with one of two endings. Most nouns take the ending -t, as in the word máryat "her hands" (two hands, a pair of hands) in Namárië. "Two ships, a couple of ships" is likewise ciryat (cirya "ship"). But if the last consonant of the stem is t or d, the ending -u is preferred: Alda "tree", Aldu "the Two Trees". In the other cases, a t is somehow inserted into or added to the various endings; for instance, the endings -ssë, -nna and -llo for locative, allative and ablative, respectively, turn into -tsë, -nta and -lto (ciryatsë, ciryanta, ciryalto = "on/to/from a couple of ships"). The instrumental ending -nen becomes -nten, while the dative ending -n becomes -nt (ciryant "for a couple of ships" - this is, by the way, the sole known case of a consonant cluster being allowed at the end of a word in Quenya).
These, then, are the Quenya case endings:
Nominative: Sg. no ending, pl. -r or -i, part.
pl. -li (Book Quenya -lí), dual -t or -u.
Accusative (in Book Quenya only): Sg. lengthening of the final vowel (if any), pl. -i, part. pl. lí, dual: probably lengthening of the final u to ú (no distinct accusative in the case of t-duals?)
Dative: Sg. -n, pl. -in, part.pl. -lin, dual -nt (but possibly -en following a dual in -u)
Genitive: Sg. -o, pl. -on (added to the nom.pl.), part.pl. -lion, dual -to.
Possessive: Sg. -va, pl. -iva, part.pl. -líva, dual -twa.
Locative: Sg. -ssë, pl. -ssen, part.pl. -lisse(n), dual -tsë.
Allative: Sg. -nna, pl. -nnar, part.pl. -linna(r), dual -nta.
Ablative: Sg. -llo, pl. -llon or -llor, part.pl. -lillo(n), dual -lto.
Instrumental: Sg. -nen, pl. -inen, part.pl. -línen, dual -nten.
Respective: Sg. -s, pl. -is, part.pl. -lis, dual -tes.
Examples of quenya nouns fully inflected