Официант подаст нам чай после ужина.

Подаст is future here.

It comes from the verb подать, which is a perfective verb. In Russian, perfective verbs do not normally have a true present tense. Their present-looking forms are used with future meaning.

So:

• подать = perfective, to serve / hand / give as a completed action
• подаст = he/she will serve

This fits the sentence because it describes one completed action in the future: the waiter will serve the tea after dinner.

Compare:

• официант подаёт чай = the waiter serves / is serving tea
  
  • from подавать (imperfective)
• официант подаст чай = the waiter will serve tea
  
  • from подать (perfective)

Нам is the dative case of мы (we).

Russian uses the dative for the person who receives something. In this sentence, tea is being served to us, so Russian says:

• подаст нам чай = will serve us tea / will serve tea to us

Case forms here:

• мы = we
• нас = us (accusative/genitive)
• нам = to us (dative)

So нам is correct because we are the indirect object, the recipients.

Чай is the direct object, so it is in the accusative case.

But for masculine singular inanimate nouns, the accusative often looks exactly the same as the nominative.

So:

• nominative: чай
• accusative: чай

That is why there is no visible change.

Compare with an animate masculine noun:

• я вижу стол = I see a table
  
  • стол is inanimate, so accusative = nominative
• я вижу брата = I see my brother
  
  • брат is animate, so accusative changes

Because после always requires the genitive case.

So:

• ужин = dinner
• ужина = of dinner / after dinner form, because genitive is needed after после

This is a very common pattern:

• после урока = after the lesson
• после работы = after work
• после ужина = after dinner

So the important point is:

• после + genitive

Официант is in the nominative case because it is the subject of the sentence — the person doing the action.

Structure of the sentence:

• Официант = subject, nominative
• подаст = verb
• нам = indirect object, dative
• чай = direct object, accusative
• после ужина = time expression, with ужина in the genitive after после

Russian has no articles.

So официант can mean:

• the waiter
• a waiter

and чай can mean:

• tea
• the tea
• sometimes even some tea, depending on context

English must choose an article, but Russian usually leaves that information to context.

So in a restaurant situation, Официант подаст нам чай после ужина naturally sounds like The waiter will serve us tea after dinner, but the Russian sentence itself does not explicitly mark the.

Yes. Russian word order is more flexible than English word order because cases show the grammatical roles.

The sentence as written is a neutral order:

• Официант подаст нам чай после ужина.

But other orders are possible, depending on emphasis:

• Нам официант подаст чай после ужина.
  Emphasis on to us
• Чай официант подаст нам после ужина.
  Emphasis on tea
• После ужина официант подаст нам чай.
  Emphasis on after dinner

The original sentence is a very natural, straightforward way to say it.

It can mean several related things, depending on context:

• to hand
• to pass
• to give
• to serve (especially food or drink)

In a restaurant sentence like this, подаст чай is naturally understood as will serve tea or will bring/serve us tea.

So the restaurant context makes serve the best translation, even though the verb itself is broader than just that one English word.

Because the sentence describes one complete future action:

• first dinner happens
• then the waiter serves the tea

Russian typically uses a perfective verb for a single completed event in the future.

So:

• подаст = will serve, as one completed act

If you used an imperfective verb, the meaning would shift. For example:

• официант будет подавать нам чай после ужина
  = the waiter will be serving us tea after dinner / will serve tea repeatedly or in a more process-focused way

In this sentence, the simple one-time action is the most natural idea, so подаст works well.

The main stresses are:

• официа́нт
• пода́ст
• нам
• чай
• по́сле
• у́жина

So you could say it roughly like this:

• официа́нт пода́ст нам чай по́сле у́жина

This matters because Russian stress is unpredictable and can move from word to word, so it is worth learning each word with its stress.