Learn Hardcore Greek: Θέλω λίγο καφέ τώρα.

Because it refers to an indefinite quantity of a mass noun. In Greek, mass nouns used in an indefinite sense normally take no article. So θέλω λίγο καφέ = “I want some coffee.” If you mean one serving (a cup), you use the indefinite article: θέλω έναν καφέ = “I want a coffee.”

What’s the difference between λίγο καφέ and έναν καφέ?

λίγο καφέ = some coffee (an unspecified amount, like a top-up or a little bit).
έναν καφέ = one coffee (a single serving/cup).

Why is it καφέ and not καφές here?

Καφέ is the form used in the oblique cases (accusative/genitive) of the masculine noun ο καφές. As the direct object of θέλω, the noun is in the accusative: with the article it would be τον καφέ; without the article (as a mass, indefinite amount) it appears simply as καφέ.

What part of speech is λίγο here?

It’s the neuter singular form of the adjective λίγος used as a quantifier (“a little, a small amount of”) before a mass noun: λίγο καφέ, λίγο νερό, λίγο ψωμί. It’s not the adverbial “a little” of time/degree (as in “wait a little”), though that’s also written λίγο.

Could I say λίγος καφές instead?

Not after a verb as a direct object. Λίγος καφές is nominative (subject), e.g., Λίγος καφές έμεινε (“A little coffee remained”). After θέλω, you need the accusative quantifier + mass noun: θέλω λίγο καφέ.

Is Θέλω λίγο καφέ τώρα polite, or does it sound too direct?

It’s quite direct and fine with friends/family. To be polite (e.g., to a server), soften it:

Θα ήθελα λίγο καφέ, παρακαλώ.
Μπορώ να έχω λίγο καφέ;
Μου βάζετε λίγο καφέ, παρακαλώ;

What about Ήθελα—can the imperfect make it more polite?

Yes. Greek often uses the imperfect to soften requests:

Ήθελα λίγο καφέ, παρακαλώ. ≈ “I was wanting / I’d like some coffee.”

Can I move τώρα around? Are these orders all correct?

Yes. Word order is flexible, with slight changes in emphasis:

Θέλω λίγο καφέ τώρα. (neutral)
Τώρα θέλω λίγο καφέ. (emphasis on “now”)
Θέλω τώρα λίγο καφέ. (also acceptable; focus stays on “now”)

How do I pronounce the sentence?

Θέλω: THEH-lo (θ like English “th” in “think”; stress on the first syllable)
λίγο: LEE-gho (γ before ο is a voiced “gh” [ɣ]; stress on the first)
καφέ: ka-FE (stress on the last)
τώρα: TO-ra (rolled/flapped ρ; stress on the first) Accents mark the stressed syllable.

Why do these words have accent marks?

In modern (monotonic) Greek, almost every polysyllabic word has exactly one stress mark on the stressed syllable. Here: Θέλω, λίγο, καφέ, τώρα. Most monosyllables aren’t accented unless needed to avoid ambiguity.

Where’s the subject pronoun? Should it be Εγώ θέλω?

Greek usually drops subject pronouns because verb endings show the person. Θέλω already means “I want.” Use Εγώ θέλω… only for emphasis/contrast: “I (as opposed to others) want…”

How do I say “I don’t want any (more) coffee now”?

“I don’t want any coffee now”: Δεν θέλω καφέ τώρα.
“I don’t want any more coffee now”: Δεν θέλω άλλο καφέ τώρα.

Can I say Θέλω να πιω καφέ τώρα? What’s the nuance?

Yes. Θέλω να πιω καφέ τώρα (“I want to drink coffee now”) makes the action explicit. Θέλω καφέ τώρα is shorter and more colloquial, common when ordering or asking for coffee.

Is καφέ ever an adjective meaning “brown”? How do I tell?

Yes. καφέ is also an indeclinable adjective meaning “brown” (e.g., καφέ παλτό = brown coat). In your sentence, context and the presence of λίγο before it show it’s the noun “coffee” (ο καφές).

What are the basic forms of καφές?

Singular: ο καφές (nom), του καφέ (gen), τον καφέ (acc)
Plural: οι καφέδες (nom), των καφέδων (gen), τους καφέδες (acc) For “two coffees (servings)”: δύο καφέδες.

Can I omit τώρα?

Yes. Θέλω λίγο καφέ. just leaves out the “now.” Add τώρα only if timing matters or for emphasis.

Are there softer/more colloquial ways to say “a little (bit)”?

Yes:

λιγάκι (a tiny bit): Θέλω λιγάκι καφέ.
Diminutive for tone: καφεδάκι (“a little coffee”/“a nice coffee”): Θέλω ένα καφεδάκι. This sounds friendly/affectionate rather than literal size.