Когда я возвращаюсь домой, собака радостно виляет хвостом.

Because Когда я возвращаюсь домой is a subordinate clause introduced by когда.

Russian normally separates this kind of time clause from the main clause with a comma:

• Когда я возвращаюсь домой, собака радостно виляет хвостом.

This works like English When I come home, the dog wags its tail happily.

If the order were reversed, you would still use a comma:

• Собака радостно виляет хвостом, когда я возвращаюсь домой.

Here the present tense expresses a habitual or repeated action.

So the sentence means something like:

• Whenever I come back home, the dog happily wags its tail.

Russian often uses the imperfective present for repeated actions like this. It does not necessarily mean only right now at this exact moment.

Because возвращаюсь is imperfective, and it fits a repeated, ongoing, habitual situation.

• возвращаюсь = I return / I am returning / I keep coming back
• вернусь = I will return once, in the future

So:

• Когда я возвращаюсь домой... = When/whenever I come back home... as a usual pattern
• Когда я вернусь домой... = When I return home... one specific future time

If you wanted a one-time future version, you might say:

• Когда я вернусь домой, собака радостно завиляет хвостом.

That is the reflexive ending.

The verb is возвращаться. In this form, it means to return, to come back.

Compare:

• возвращать = to return something, to give back
• возвращаться = to return oneself, to come back

So я возвращаюсь домой means I am coming back home.

The reflexive ending is:

• -ся after most consonants
• -сь after vowels and some verb endings

That is why you get возвращаюсь.

Because домой means homeward / to home, showing motion toward home.

Compare:

• домой = to home, homeward
• дома = at home

So:

• Я возвращаюсь домой = I am returning home
• Я дома = I am at home

This is a very common contrast in Russian and is worth memorizing as a set.

Yes, you could, but the nuance changes a little.

• прихожу домой focuses on arriving home
• возвращаюсь домой focuses on coming back / returning home

So both can work, but возвращаюсь suggests that you were away and are now returning. That makes it especially natural here.

Russian has no articles like the or a.

So собака can mean:

• a dog
• the dog

The exact meaning depends on context.

In this sentence, English naturally uses the dog because it sounds like a known, specific dog. Russian does not need a separate word for that.

Because the noun хвостом is in the instrumental case.

With вилять, Russian often uses the instrumental to express the body part or thing being moved:

• вилять хвостом = to wag one’s tail
• literally, something like to wag with the tail

So:

• хвост = nominative
• хвостом = instrumental

This is a normal pattern and should be learned together with the verb:

• вилять хвостом

Радостно is an adverb. It describes how the dog wags its tail.

So:

• радостный = joyful, happy
• радостно = joyfully, happily

It modifies the verb phrase:

• собака радостно виляет хвостом = the dog happily wags its tail

In Russian, adverbs often end in -о.

Yes. Russian word order is fairly flexible, because case endings help show grammatical roles.

The neutral order here is:

• Когда я возвращаюсь домой, собака радостно виляет хвостом.

But other orders are possible for emphasis, for example:

• Когда я возвращаюсь домой, радостно виляет хвостом собака.
• Собака, когда я возвращаюсь домой, радостно виляет хвостом.

These may sound more marked or literary depending on context. For a learner, the original version is the most natural and safest.

Yes, often it can be omitted, because the verb ending already shows the person:

• возвращаюсь = I return / I am returning

So you could say:

• Когда возвращаюсь домой, собака радостно виляет хвостом.

That is possible and natural in the right context. But keeping я is also completely normal, especially if you want clarity or emphasis.

Then you would normally switch to perfective future forms.

A natural version would be:

• Когда я вернусь домой, собака радостно завиляет хвостом.

Why?

• вернусь = I will return
• завиляет = will start wagging / will wag

This version means one concrete future event, not a habitual pattern.

So the contrast is:

• Когда я возвращаюсь домой, собака радостно виляет хвостом. = whenever I come home
• Когда я вернусь домой, собака радостно завиляет хвостом. = when I get home on that future occasion