Ben bugün çok yorgunum, bu yüzden evde kalıyorum.

Yes, ben can be left out.

Turkish verbs usually show the subject through their endings, so yorgunum already means I am tired, and kalıyorum already means I am staying / I stay.

So these are both natural:

• Ben bugün çok yorgunum, bu yüzden evde kalıyorum.
• Bugün çok yorgunum, bu yüzden evde kalıyorum.

Including ben adds a little emphasis, like as for me or I in contrast to someone else.

Bugün means today.

In this sentence, it tells you when the speaker is tired. Turkish word order is fairly flexible, so bugün does not have to stay exactly there.

For example, these are all possible:

• Ben bugün çok yorgunum.
• Bugün ben çok yorgunum.
• Çok yorgunum bugün.

The version in your sentence is just a very natural, neutral order.

Yorgunum is made of:

• yorgun = tired
• -um = I am

So yorgunum literally means I am tired.

This is very common in Turkish: adjectives can act like complete predicates by taking personal endings.

Examples:

• Mutluyum = I am happy
• Hazırım = I am ready
• Yorgunum = I am tired

So Turkish does not need a separate word like am here.

It is the 1st person singular personal ending, meaning I.

The exact shape of the ending changes because of vowel harmony. After yorgun, the correct form is -um, giving yorgunum.

You do not need to memorize every detail at once, but the key idea is:

• yorgun + um → yorgunum

Similar examples:

• iyiyim = I am well
• üzgünüm = I am sad
• memnunum = I am pleased

Bu yüzden means because of this, therefore, or so.

In this sentence, it links the two ideas:

• I am very tired today
• therefore / so I am staying at home

So it shows a result.

A very similar expression is o yüzden, which is also extremely common in everyday Turkish. In many situations, bu yüzden and o yüzden are both possible, though o yüzden is often especially common in speech.

Evde means at home / in the house.

It is built from:

• ev = house / home
• -de = in / at (location suffix)

So Turkish often uses a case ending instead of a separate preposition like English does.

Examples:

• evde = at home
• okulda = at school
• işte = at work
• masada = on the table / at the table depending on context

So Turkish does not need a separate word for at here, because -de already expresses location.

Kalıyorum comes from kalmak, which means to stay / remain.

The form -iyor is often called the present continuous, but in Turkish it covers both meanings that English often separates:

• I am staying
• I stay

In this sentence, evde kalıyorum is best understood as I’m staying home or I’m staying at home.

Because of context, it sounds like a present decision or current action resulting from being tired.

In Turkish, the idea of am/is/are is often built into the ending rather than expressed as a separate word.

So:

• Ben yorgunum = I am tired
• Sen yorgunsun = You are tired
• O yorgun = He/She is tired

This is why yorgunum already contains the meaning am.

English uses a separate verb (am), but Turkish often does not.

Çok means very here, and it modifies yorgunum.

So:

• çok yorgunum = I am very tired

In other contexts, çok can also mean much or a lot, depending on what it is describing.

Examples:

• çok güzel = very beautiful
• çok çalışıyorum = I work a lot
• çok su = a lot of water

In your sentence, it clearly means very.

Yes. Turkish allows some flexibility.

Your sentence is:

• Ben bugün çok yorgunum, bu yüzden evde kalıyorum.

A natural alternative is:

• Bugün çok yorgunum, bu yüzden evde kalıyorum.

You could also express the same idea in other ways, for example:

• Bugün çok yorgun olduğum için evde kalıyorum.
  = Because I am very tired today, I am staying at home.

So the exact structure can change, even when the meaning stays similar.

The comma is natural and helpful here because the sentence has two parts:

• Ben bugün çok yorgunum
• bu yüzden evde kalıyorum

The comma shows a pause before the result clause.

In informal writing, people may sometimes omit it, but using it here is perfectly normal and clear.

Yes. The verb kalmak has a range of meanings including stay, remain, and sometimes be left depending on context.

In this sentence:

• evde kalıyorum

most naturally means I’m staying home or I’m staying at home.

The exact English translation depends on context, but the Turkish is very natural for the idea that the speaker chooses not to go out because they are tired.

It is neutral and natural. It works well in everyday conversation and normal writing.

Nothing in it is slangy or overly formal. It is the kind of sentence a Turkish speaker could easily say in daily life:

• Ben bugün çok yorgunum, bu yüzden evde kalıyorum.

So it is a very good model sentence for learners.