После ужина лучше сразу убрать со стола тарелки.

Because после always takes the genitive case.

• ужин = dinner
• после ужина = after dinner

So ужина is the genitive singular form of ужин.

Similar examples:

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

Here лучше means something like:

• it’s better to...
• you’d better...
• it is best to...

So После ужина лучше сразу убрать со стола тарелки means:

• After dinner, it’s better to clear the plates from the table right away.

In Russian, лучше is often used in this impersonal way with an infinitive:

• Лучше подождать. = It’s better to wait.
• Лучше не спорить. = It’s better not to argue.

Russian often leaves the subject unstated when the meaning is general or obvious from context.

So this sentence does not literally say who should do it. It just gives general advice:

• После ужина лучше сразу убрать со стола тарелки.
• After dinner, it’s better to clear the plates from the table right away.

In English, we often need a subject, but Russian can sound completely natural without one in this kind of statement.

Because after лучше in this structure, Russian commonly uses an infinitive.

Pattern:

• лучше + infinitive

Examples:

• Лучше уйти сейчас. = It’s better to leave now.
• Лучше позвонить завтра. = It’s better to call tomorrow.

So:

• лучше убрать = it’s better to clear away / remove

Убрать is the perfective form, and убирать is the imperfective form.

Here the sentence is about completing one action:

• clear the plates away
• get that done

That is why убрать sounds natural.

Compare:

• лучше убрать тарелки = it’s better to clear the plates away
  (focus on completing the action)
• лучше убирать тарелки сразу = it’s better to clear plates right away / as a habit
  (more about a repeated or general process)

In this sentence, the idea is a practical recommendation about a completed action after dinner, so убрать fits well.

Сразу means:

• right away
• immediately
• at once

In this sentence:

• лучше сразу убрать = it’s better to clear them away right away

Its position is flexible, but putting it before the infinitive is very common because it modifies the action:

• лучше сразу убрать тарелки
• лучше убрать тарелки сразу

Both are possible, though the first sounds especially natural here.

This is the preposition с / со meaning from, used with the genitive case to show removal from a surface or place.

• стол = table
• со стола = from the table

The form стола is genitive singular.

Why со instead of с?
Russian sometimes uses со instead of с for easier pronunciation. Before certain consonant clusters, со sounds smoother.

So:

• со стола = from the table

This is a very common phrase:

• взять со стола = take from the table
• убрать со стола = clear off the table

Тарелки here is accusative plural of тарелка.

• singular: тарелка = plate
• plural: тарелки = plates

Since убрать is acting on the plates, тарелки is the direct object, so it should be in the accusative.

For inanimate plural nouns, the accusative is usually the same as the nominative:

• nominative plural: тарелки
• accusative plural: тарелки

So the form does not change.

Both word orders are possible:

• убрать со стола тарелки
• убрать тарелки со стола

Russian word order is more flexible than English.

In this sentence, убрать со стола тарелки sounds natural and puts a little more focus on the idea of clearing them off the table.

Meanwhile:

• убрать тарелки со стола sounds slightly more straightforwardly object-first: clear the plates off the table.

Both are correct.

Literally, it means remove the plates from the table.

In context, it usually suggests part of the normal action of clearing the table after eating. But strictly speaking, the sentence mentions only тарелки = plates, not cups, cutlery, napkins, and so on.

If Russian wanted to say something broader, it might use:

• убрать со стола посуду = clear the dishes from the table
• убрать со стола всё = clear everything off the table

Yes, that is a very natural English translation.

Even though the Russian sentence literally uses a more impersonal structure:

• После ужина лучше сразу убрать со стола тарелки.
• After dinner, it’s better to clear the plates off the table right away.

In natural English, You should clear the plates off the table right after dinner often conveys the same idea.

Just remember that the Russian sentence sounds slightly more like general advice than a direct command.

No. Even in fast speech, the grammar is still после ужина.

Russian case endings are important, and native speakers do hear the difference. A learner might not always catch every ending clearly at first, but the correct form after после is still the genitive:

• после завтрака = after breakfast
• после обеда = after lunch
• после ужина = after dinner

So you should definitely learn and use после + genitive.