صديقي يدرس العربية في الجامعة.

A common reading is:

ṣadīqī yadrusu al-ʿarabiyyata fī al-jāmiʿati

Word by word:

• صديقي = ṣadīqī
• يدرس = yadrusu
• العربية = al-ʿarabiyyata
• في = fī
• الجامعة = al-jāmiʿati

In normal Arabic writing, the short vowels are usually not written, so learners have to know them from grammar and vocabulary.

صديق means friend.

To say my friend, Arabic adds the suffix ـي meaning my:

• صديق = friend
• صديقي = my friend

So Arabic does not use a separate word for my here. It attaches it directly to the noun.

This is also an example of the construct state (iḍāfa), where the noun becomes connected to the possessor suffix.

Because the verb itself already tells you the subject.

يدرس means he studies or he is studying.
So Arabic does not need an extra pronoun like هو unless you want emphasis or contrast.

• يدرس = he studies
• هو يدرس = he is studying / he studies, with extra emphasis on he

In this sentence, صديقي already tells us who the subject is, so a separate pronoun would be unnecessary.

يدرس is a present-tense verb, specifically:

• 3rd person
• masculine
• singular

So it means he studies or he is studying.

It comes from the root د-ر-س, which is connected with studying/learning.

Related forms:

• أدرس = I study
• تدرس = you study / she studies
• ندرس = we study
• يدرس = he studies

It can mean either one, depending on context.

In Modern Standard Arabic, the present tense often covers both:

• he studies
• he is studying

So صديقي يدرس العربية في الجامعة could mean:

• My friend studies Arabic at the university
• My friend is studying Arabic at the university

English makes a bigger distinction here than Arabic usually does.

Here العربية means Arabic as a language/subject.

In Arabic, language names are very often used with الـ in sentences like this:

• أدرس العربية = I study Arabic
• يُعلِّم العربية = he teaches Arabic

So العربية here is the normal way to say Arabic as the subject being studied.

Also, this word is historically an adjective meaning Arabic (feminine), but it is commonly used as a noun meaning the Arabic language.

Because the word العربية is short for اللغة العربية:

• اللغة = the language
• العربية = Arabic

Since لغة is feminine, the adjective عربية is feminine too. Over time, Arabic often drops اللغة and just keeps العربية, which then means the Arabic language.

So even though English says simply Arabic, Arabic often uses this feminine form.

في means in or at.
الجامعة means the university.

So في الجامعة means in the university or more naturally in English, at the university.

Arabic often uses the in places where English may sound more natural without it or with a more general expression.

Arabic commonly uses the definite article in this kind of phrase:

• في الجامعة = at the university
• في المدرسة = at school
• في البيت = at home / in the house

So الـ here is completely normal. Arabic and English do not always use the definite article in the same way.

Arabic allows more than one word order.

This sentence uses subject + verb + object:

• صديقي يدرس العربية

But Arabic can also use verb + subject + object:

• يدرس صديقي العربية

Both are possible. Very roughly:

• صديقي يدرس... can feel a little more like My friend studies...
• يدرس صديقي... can feel a little more like My friend is studying... with the action presented first

In real usage, both are normal. Learners should get used to both patterns.

A fully vowelled version is:

صديقي يدرسُ العربيةَ في الجامعةِ

Here is what is happening:

• صديقي = subject, so it is nominative, but the case ending is not clearly visible in the usual spelling because of the ـي possessive ending
• يدرسُ = present tense indicative, so it ends in ـُ
• العربيةَ = direct object, so it is accusative, ending in ـَ
• في الجامعةِ = after the preposition في, the noun is genitive, ending in ـِ

So the visible grammatical endings are:

• يدرسُ
• العربيةَ
• الجامعةِ

It is definite.

Anything with a possessive suffix like ـي (my) is automatically definite:

• كتاب = a book
• كتابي = my book
• صديق = a friend
• صديقي = my friend

So صديقي means a specific friend: my friend.

The object is العربية because it is the thing being studied.

So:

• صديقي = the subject, the person doing the action
• يدرس = the action
• العربية = the object, what he studies
• في الجامعة = a prepositional phrase telling where

In a fully vowelled sentence, the accusative ending on العربيةَ also helps identify it as the direct object.

In both words, the ل of الـ is pronounced clearly:

• al-ʿarabiyya
• al-jāmiʿa

That is because ع and ج are moon letters, not sun letters.

So you say:

• العربية = al-ʿarabiyya
• الجامعة = al-jāmiʿa

There is no doubling of the next consonant here.

Yes. In fact, that is the normal way Arabic is usually written.

So normally you write:

صديقي يدرس العربية في الجامعة

If you add full vowel marks for learning or formal grammatical illustration, it could look like:

صديقي يدرسُ العربيةَ في الجامعةِ

Both represent the same sentence; the second just shows more pronunciation and grammar information.