На столе уже стоят рамка и ваза, а мама думает, куда поставить цветы.

Because на столе answers the question where? and uses the prepositional case after на.

• на столе = on the table
• на стол = onto the table

So in this sentence, the frame and vase are already located there, which is why Russian uses на столе.

Because the subject is actually рамка и ваза — the frame and the vase — which is plural as a whole.

Even though each noun is singular, together they form a plural subject, so Russian uses:

• стоит = stands / is standing (singular)
• стоят = stand / are standing (plural)

So:

• рамка стоит = the frame is standing
• ваза стоит = the vase is standing
• рамка и ваза стоят = the frame and the vase are standing

Russian word order is much freer than English word order. The normal English order would be The frame and the vase are already on the table, but Russian can very naturally say:

• На столе уже стоят рамка и ваза

This structure often presents the location first, and then introduces what is there. It feels a bit like:

• On the table there already stand a frame and a vase

So the order is natural and common in Russian.

Because they are the subject of the verb стоят, so they are in the nominative case.

• рамка = frame
• ваза = vase

Nothing is being done to them; they are the things that are standing on the table.

Уже means already.

In this sentence:

• На столе уже стоят рамка и ваза = There is already a frame and a vase on the table

Russian allows some flexibility in the position of уже, but here it naturally modifies the whole situation: the frame and vase are already there.

А often connects two clauses with a mild contrast or change of focus. It does not always mean a strong but, but it often has that flavor.

Here:

• На столе уже стоят рамка и ваза, а мама думает...

This gives the idea:

• The frame and vase are already on the table, but/as for Mom, she is thinking...

So а helps shift attention from the objects on the table to what Mom is thinking.

Because куда means to where? / where to?, which involves direction or destination.

Mom is thinking about where to put the flowers — that is, to what place they should be moved.

Compare:

• где = where? (location)
• куда = where to? (destination)
• откуда = from where?

So:

• где стоят цветы? = Where are the flowers standing?
• куда поставить цветы? = Where should I put the flowers?

Because it depends on думает.

Russian often uses this structure:

• думать, что сделать / куда пойти / как сказать
• to think about what to do / where to go / how to say it

So мама думает, куда поставить цветы literally means:

• Mom is thinking where to put the flowers

The infinitive поставить expresses the action she is considering.

This is a question of aspect.

• ставить = imperfective, focusing on process or repeated action
• поставить = perfective, focusing on a single completed action

Here Mom is thinking about one concrete act of placing the flowers somewhere, so поставить is the natural choice.

Compare:

• Она любит ставить цветы на окно. = She likes putting flowers on the windowsill. / She likes to place flowers there.
• Она думает, куда поставить цветы. = She is thinking where to put the flowers.

Here цветы is accusative plural, because it is the object of поставить.

But for many inanimate plural nouns, the accusative plural looks exactly the same as the nominative plural.

So:

• nominative plural: цветы = flowers
• accusative plural: цветы = flowers

That is why the form does not change here.

Russian often repeats the noun where English might use she. This can make the sentence clearer and more natural, especially when introducing a new clause or shifting focus.

So:

• ..., а мама думает... = ..., and Mom is thinking...

Russian could also use a pronoun in some contexts, but repeating мама is completely normal.

Russian often uses more specific verbs of position where English simply uses is/are.

• стоять = to stand
• лежать = to lie
• висеть = to hang
• сидеть = to sit

A vase normally stands, and a frame can also be imagined as standing if it is upright on a table. So Russian prefers стоят rather than a general equivalent of are.

This is a very common feature of Russian.

Usually рамка means frame, and in this kind of context it most likely means a picture frame or photo frame standing on the table.

The exact type is often left unspecified unless the context makes it important. If needed, Russian could say:

• фоторамка = photo frame

But рамка works naturally here.