После дождя я вытер воду с подоконника тряпкой.

Because the preposition после always takes the genitive.

• после = after
• дождь = rain
• genitive singular: дождя

So:

• после дождя = after the rain / after it rained

This is a very common pattern in Russian:

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

It means after the rain or, more naturally in English, after it rained.

Russian often uses a noun phrase where English might prefer a full clause. So instead of saying something like After it had rained, I..., Russian can simply say:

• После дождя... = After the rain...

It sets the time frame for the main action.

Вытер is the perfective past form, and it shows a completed action: the speaker wiped the water away successfully.

• вытер = wiped off / wiped up completely
• вытирал = was wiping / used to wipe / wiped in a process-oriented way

In this sentence, the action is presented as a finished event, so вытер is the natural choice.

Compare:

• Я вытер воду с подоконника. = I wiped the water off the windowsill.
• Я вытирал воду с подоконника. = I was wiping water off the windowsill / I wiped water off the windowsill (focus on process, not completion)

Because вода is the direct object of the verb вытер.

The speaker did the action to the water:

• dictionary form: вода
• accusative singular: воду

So:

• я вытер воду = I wiped the water

This is standard Russian direct-object marking.

These mean slightly different things.

• вытер воду с подоконника = wiped the water off the windowsill
• вытер подоконник = wiped the windowsill

In your sentence, the focus is specifically on removing the water, not just cleaning the surface in general.

So the structure is:

• вытер [что?] воду
• с [чего?] с подоконника

Literally: wiped the water from the windowsill

It is genitive singular after the preposition с in the meaning from/off.

Here, с means from or off:

• с подоконника = from the windowsill / off the windowsill

The noun is:

• подоконник = windowsill
• genitive singular: подоконника

This is a common pattern with verbs of removing something from a surface or place:

• снять книгу со стола = take the book off the table
• стереть пыль с полки = wipe dust off the shelf
• убрать чашку с подоконника = remove the cup from the windowsill

Because the instrumental case is often used to show the tool or means used to do something.

• тряпка = rag / cloth
• instrumental singular: тряпкой

So:

• тряпкой = with a rag / using a rag

This is a very common use of the instrumental:

• писать ручкой = write with a pen
• резать ножом = cut with a knife
• мыть губкой = wash with a sponge

Yes, depending on context, but Russian does not have articles, so тряпкой by itself does not tell you whether it is:

• with a rag
• with the rag
• sometimes even using some cloth

You choose the English article from context. If the rag has not been mentioned before, with a rag is usually the most natural translation.

The basic order here is:

• После дождя — time expression
• я — subject
• вытер — verb
• воду — direct object
• с подоконника — source/place removed from
• тряпкой — instrument

Russian word order is flexible, so other versions are possible, such as:

• Я после дождя вытер воду с подоконника тряпкой.
• Тряпкой я вытер воду с подоконника после дождя.

But the original sounds natural and neutral. Putting После дождя first is very common because it sets the scene: after the rain.

Because Russian has no articles like a or the.

Russian simply says:

• дождя
• воду
• подоконника
• тряпкой

Whether English should use a, the, or no article at all depends on the context and on natural English style.

So the Russian sentence does not separately mark:

• after rain vs after the rain
• water vs the water
• with a rag vs with the rag

English has to supply that information.

Подоконник means windowsill.

It comes from:

• под = under
• окно = window

Historically, it is something like the part under the window. In modern Russian, it simply means the windowsill or window ledge.

So:

• с подоконника = off the windowsill

Not necessarily. Russian often uses a singular mass noun where English also uses a mass noun:

• вода = water

It does not count separate drops or puddles. The sentence just means there was water on the windowsill, and the speaker wiped it off.

So воду here is completely natural even if there was quite a lot of water.

Yes. Russian often leaves that kind of thing unstated because it is obvious.

После дождя simply gives the situation: it had rained, and then the next action happened. Russian does not need to say:

• после того, как пошёл дождь
• после того, как дождь закончился

unless the speaker wants to be more specific.

So in normal speech, После дождя is a very natural and efficient way to say after the rain or after it rained.