Learn Hardcore Romanian: Ana spune că vrea cafea fără lapte. - Ana says that she wants coffee without milk.

spune is the third-person singular present of a spune (to say). Conjugation in the present is: eu spun, tu spui, el/ea spune, noi spunem, voi spuneți, ei/ele spun. Here it means “Ana says.”

Why is că used, and can it be omitted?

că functions like English that, introducing the subordinate clause: “Ana says that she wants coffee….” In standard Romanian you need că for clarity. Very informal speech might drop it, but that sounds abrupt or unclear. For direct quotation you’d write:
Ana spune: “Vreau cafea fără lapte.”

Why is there no să before vrea, and how does vrea work here?

vrea is the third-person singular present of a vrea (to want). When the object of vrea is a noun (like cafea), you simply say vrea cafea (“wants coffee”). You only add să when the object is a verb:
Ana vrea să bea cafea = “Ana wants to drink coffee.”

Why isn’t there an article before cafea, and when would you use o cafea or niște cafea?

Here cafea is used generically/uncountably (“coffee” in general), so no article is needed. If you want one cup, say o cafea (“a coffee”). For an unspecified amount, use niște cafea (“some coffee”).

Why doesn’t fără require an article before lapte?

The preposition fără (“without”) always takes the noun in its bare form, without any article or determiner: fără lapte, fără zahăr, fără sare, etc.

What gender is lapte, and why is it article-free here?

lapte is a neuter noun (behaves like masculine in singular and feminine in plural). As with cafea, here it’s an uncountable substance (“milk”), so no article. If you specify quantity, you’d say something like un litru de lapte (“a liter of milk”).

How do you pronounce Ana spune că vrea cafea fără lapte?

Phonetically:
Ana [ˈa.na]
spune [ˈspu.ne] (“SPOO-neh”)
că [kə] (“kuh”)
vrea [ˈvre.a] (“VREH-ah”)
cafea [kaˈfe̯a] (“ka-FEH-ah”)
fără [ˈfərə] (“FUH-ruh”)
lapte [ˈlap.te] (“LAHP-teh”)