Learn Hardcore Danish: Jeg beder om et glas vand.

spørge om = ask about a topic: Jeg spørger om åbningstiderne. (I’m asking about the opening hours.)
spørge efter = ask after/for someone or something’s whereabouts: Jeg spørger efter chefen. (I’m asking for the boss.)
To request an item, use bede om or common request formulas like Kan jeg få…? or Jeg vil gerne have…

Is Jeg beder om et glas vand the most natural way to order?

It’s correct but can sound a bit formal or stiff in everyday situations. More typical options:

Jeg vil gerne have et glas vand.
Kan jeg få et glas vand?
Må jeg få et glas vand?
Må jeg bede om et glas vand? (polite)
Et glas vand, tak. (very common and polite)

Why is it et and not en?

Because glas is a neuter noun in Danish. Neuter nouns take et in the indefinite singular.

Singular: et glas
Definite singular: glasset
Indefinite plural: glas
Definite plural: glassene

Why is there no article before vand?

Vand is an uncountable mass noun. After a measure/container noun like glas, you don’t add an article:

et glas vand, en flaske vand, en kop kaffe, etc. You can say noget vand (“some water”) on its own, and the definite form is vandet (“the water”).

Where should I put tak to be polite?

Add it at the end (or the beginning) of the request:

Et glas vand, tak.
Kan jeg få et glas vand, tak? Starting with Tak, is also fine: Tak, et glas vand.

Where does the negation ikke go?

Place ikke after the finite verb (and subject), before the prepositional phrase:

Jeg beder ikke om et glas vand. With other adverbs (kun, bare, lige), the placement is the same:
Jeg beder kun om et glas vand.

How do you pronounce the sentence?

Very rough guide (English-friendly):

Jeg ≈ “yai”
beder ≈ “BEH-ther,” where the Danish d is soft, like the th in “this” ([ð]); final -er is a weak “uh” sound
om ≈ “om” (short, like “omm”)
et often reduced to a quick “e”; careful speech: “et”
glas ≈ “glas” (short “a”)
vand ≈ “van” (the d is silent) Altogether: “yai BEH-ther om e glas van”

What are the main forms of bede?

Infinitive: bede
Present: beder
Past (preterite): bad
Past participle: bedt Examples: I går bad jeg om et glas vand. / Jeg har bedt om vand.

Does bede also mean “to pray”? How would I say that?

Yes. Without om, bede most often means “to pray.”

Jeg beder. (I’m praying.)
bede til = pray to: Hun beder til Gud.
bede for = pray for: Vi beder for ham. Be careful: bede om = ask for/request.

How would I turn it into a direct question?

Use verb-second word order:

Yes/No: Beder du om et glas vand?
Wh-question: Hvad beder du om?

Can I front the object for emphasis?

Grammatically yes:

Et glas vand beder jeg om. But in everyday speech it sounds marked or literary. For natural emphasis, most people would choose a different formulation, e.g. Jeg vil virkelig gerne have et glas vand.

Should I use glas or kop?

For water, use glas.

glas = glass (cold drinks: water, juice, soda)
kop = cup (hot drinks: coffee, tea)
krus = mug

How can I specify tap, still, or sparkling water?

Tap water: postevand — Et glas postevand, tak.
Still bottled water: kildevand — En kildevand, tak.
Sparkling water: danskvand — En danskvand, tak.

Do people say en vand?

Colloquially, yes—in cafés/bars en vand often means “a bottled water.” Strictly, vand is neuter as a mass noun (vandet), but in this beverage sense many speakers use the common-gender pattern. For a tap-water portion, say et glas (poste)vand.

What’s the pattern if I want to “ask someone for something” or “ask someone to do something”?

Use:

bede nogen om noget: Jeg beder tjeneren om et glas vand.
bede nogen om at + infinitiv: Jeg beder dig om at sende regningen.