Learn Hardcore Swedish: Vi köper kaffe åt våra gäster.

kaffe for coffee in general or an unspecified amount.
kaffet for a specific, known coffee (the coffee).
In cafés, you may hear en kaffe to mean “a coffee (a cup).” That’s an ellipsis for en kopp kaffe and is fine in casual speech.

What’s the difference between åt, till, and för when they translate to “for/to”?

åt: beneficiary/on someone’s behalf. With köpa, it’s very common: köpa något åt någon (buy something for someone).
till: direction/recipient. Also common with köpa when you plan to give/serve the item: köpa kaffe till gästerna.
för: reason, price, or “for the sake of,” not the typical beneficiary with köpa.
- Price: Vi köper kaffe för 50 kronor.
- Sake/reason: Vi köper kaffe för våra gästers skull.
  In many contexts åt and till overlap with köpa; för usually does not.

Could I say Vi köper våra gäster kaffe (double object) like in English?

Not with köpa. Swedish normally needs a preposition for the indirect object here:

Natural: Vi köper kaffe åt/till våra gäster.
Unnatural: Vi köper våra gäster kaffe.

However, some verbs do allow a double-object pattern:

Vi gav gästerna kaffe. (with ge, “give”)

Why is it våra gäster and not våra gästerna?

Swedish doesn’t allow “double definiteness” with possessives. A possessive (like våra) already makes the noun definite in meaning, so the noun takes the indefinite form:

Correct: våra gäster (our guests)
Incorrect: våra gästerna

How does vår/vårt/våra agree with nouns?

The possessive agrees with the grammatical gender and number of the noun:

vår
- common-gender singular: vår bil (our car)
vårt
- neuter singular: vårt hus (our house)
våra
- any plural: våra gäster (our guests)

Parallel for “my”: min/mittt/mina.

What tense is köper, and does it cover “buy” and “are buying”?

köper is present tense and covers both simple and progressive meanings in English:

“We buy” and “We are buying” = Vi köper.

Key forms of köpa:

Infinitive: (att) köpa
Present: köper
Preterite (past): köpte
Supine (used with har/hade): köpt → Vi har köpt kaffe.

Where would I put inte (not) in this sentence?

Place inte after the finite verb in main clauses:

Vi köper inte kaffe åt våra gäster.
If you front something for emphasis, inte still follows the verb:
I dag köper vi inte kaffe åt våra gäster.

Can I change the order of kaffe and åt våra gäster?

Default is object first, then the prepositional phrase:

Neutral: Vi köper kaffe åt våra gäster.

Switching them is generally unnatural:

Odd: Vi köper åt våra gäster kaffe.

You can front the prepositional phrase for emphasis or contrast:

Emphatic/topicalized: Åt våra gäster köper vi kaffe.

Is åt here the same word as the past tense of “eat” (åt = “ate”)?

They’re spelled the same but are different words:

åt (preposition) = for/to (beneficiary).
åt (preterite of äta) = ate.
Context disambiguates them.

Is kaffe an en-word or an ett-word?

As a mass noun it doesn’t show an article: kaffe. The definite is kaffet, which indicates it’s neuter (ett) historically. In café talk, en kaffe is common to mean “a coffee (cup),” even though it’s not the dictionary gender—this is a conventional shorthand.

Does för ever work with köpa to mean “for someone”?

Not for the beneficiary. Use åt or till for “for someone.” With köpa, för typically signals price or reason:

Vi köper kaffe för 50 kronor. (price)
Vi köper kaffe för våra gästers skull. (for their sake)

What are the forms of gäst?

Singular indefinite: en gäst
Singular definite: gästen
Plural indefinite: gäster
Plural definite: gästerna
With a possessive, use the indefinite form: våra gäster, mina gäster.

Any pronunciation tips for the tricky letters and sounds?

köper: k before ö is “soft k” [ɕ], approx. “sh” but brighter; ö is a rounded front vowel [øː]. Roughly: “SHÖH-per.”
åt: long å [oː], like “awe” but rounded; “oht.”
gäster: g before ä is the “y”-like sound [j]; ä like “bed”; doubled ss is long. Roughly: “YESS-ter.”
Swedish letters å, ä, ö are distinct letters, not just variants of a and o.