На подоконнике уже стоят ваза и рамка с нашей семейной фотографией.

Because на means on, and after a preposition Russian nouns usually change form.

Here на answers the question where?, so it takes the prepositional case for location:

• подоконник = windowsill
• на подоконнике = on the windowsill

So the ending changes because the noun is part of the phrase on the windowsill, not just standing alone.

This is the prepositional singular form of a masculine noun.

For many masculine nouns ending in a consonant, the prepositional singular often ends in -е:

• стол → на столе
• город → в городе
• подоконник → на подоконнике

So подоконнике is just the correct case form after на when talking about location.

Because the subject is actually two things:

• ваза
• рамка

Together they form a plural subject: ваза и рамка = the vase and the frame

So the verb must be plural:

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

Russian often uses verbs like стоять (to stand), лежать (to lie), and висеть (to hang) where English simply says is/are.

Here стоят suggests that the vase and the frame are in an upright position on the windowsill. That sounds natural in Russian.

So Russian prefers something like:

• На подоконнике стоят... = On the windowsill there stand / there are...

rather than using a direct equivalent of English there are.

Because Russian usually does not need one in sentences like this.

English often says:

• There is a vase...
• There are two books...

Russian normally just states the location and the thing itself:

• На столе книга.
• На полке стоят чашки.

So in this sentence, На подоконнике уже стоят... naturally means something like There are already ... on the windowsill.

Уже means already.

It often appears before the verb or before the part of the sentence it modifies. Here it comes before стоят, so it gives the sense that these objects are already there now.

• На подоконнике уже стоят... = On the windowsill, ... are already standing / are already there

The exact position of уже can vary, but this placement is very natural.

Because с here means with, and Russian uses that pattern very naturally:

• рамка с фотографией = a frame with a photograph

This describes the frame as containing or going together with the photo.

If you said рамка нашей семейной фотографии, that would sound more like the frame of our family photograph, which is less natural in this context.

So рамка с фотографией is the normal way to say a frame with a photo / photo frame with our family picture.

Because after с meaning with, Russian normally uses the instrumental case.

So:

• фотография = photograph
• с фотографией = with a photograph

Here the full phrase is:

• с нашей семейной фотографией = with our family photograph

So the noun changes to instrumental because of the preposition с.

They must agree with фотографией, which is:

• feminine
• singular
• instrumental case

So the words describing it must also be feminine singular instrumental:

• наша → нашей
• семейная → семейной
• фотография → фотографией

This is standard adjective/pronoun agreement in Russian: descriptors match the noun in gender, number, and case.

By itself, рамка can mean frame in a broad sense. But in the phrase рамка с фотографией, it is naturally understood as a picture frame or photo frame.

So the context tells you what kind of frame it is.

Russian word order is more flexible than English word order.

Starting with На подоконнике puts the location first, setting the scene: As for the windowsill...

Then уже стоят tells you what is already there, and finally ваза и рамка... introduces the items.

This order is very natural if the speaker wants to emphasize the place first. English often prefers:

• A vase and a frame are already on the windowsill

But Russian can very naturally say:

• On the windowsill already stand a vase and a frame

even though that sounds less ordinary in English.

Russian has no articles like a or the.

So ваза can mean:

• a vase
• the vase

and рамка can mean:

• a frame
• the frame

You figure it out from context. In this sentence, English could translate it either way depending on the situation. Russian simply leaves that distinction unstated unless something else in the sentence makes it clear.

Here it means a family photo, that is, a photo of the family members together.

So наша семейная фотография is naturally understood as our family photograph. It does not mean just any photo owned by the family; it specifically suggests the kind of picture showing the family.