من و خواهرم دیروز یک آپارتمان نزدیک مرکز شهر دیدیم.

A careful pronunciation would be something like:

man o xâharam diruz yek âpârtemân-e nazdik-e markaz-e shahr didim

A few important notes:

• و is often pronounced o in connected speech, so من و خواهرم sounds like man o xâharam.
• Persian script usually does not write short vowels, so some sounds you hear are not visible in the spelling.
• The linking sound called ezafe is also usually not written here, but it is pronounced in phrases like مرکزِ شهر.

Yes. من و خواهرم literally means I and my sister.

This is completely normal in Persian. English style guides often prefer my sister and I, but Persian does not have the same rule. So من و خواهرم is natural and common.

The -م is a possessive ending meaning my.

So:

• خواهر = sister
• خواهرم = my sister

This is a very common pattern in Persian:

• کتابم = my book
• دوستم = my friend
• خانه‌ام / خونه‌م = my house

So instead of using a separate word for my, Persian often adds an ending to the noun.

The word و means and. In isolation or very careful speech, it may be pronounced va, but in normal speech it is very often pronounced o.

So:

• من و خواهرم is commonly pronounced man o xâharam

Both pronunciations are connected to the same written word و.

دیدیم means we saw.

It breaks down like this:

• دید- = the past stem of دیدن (to see)
• -یم = the ending for we

So:

• دیدیم = we saw

This is one reason Persian often does not need subject pronouns. The verb ending already tells you who did the action. In this sentence, though, the subject من و خواهرم is still stated for clarity.

Because یک آپارتمان is an indefinite direct object here.

In Persian, را usually marks a direct object that is definite or specific.

So:

• یک آپارتمان دیدیم = we saw an apartment
• آن آپارتمان را دیدیم = we saw that apartment

Learners often notice that English always allows a/an, but Persian also cares about whether the object is specific enough to take را.

Yes, یک can function like English a/an.

So:

• یک آپارتمان = an apartment

Persian does not have a separate article exactly like English a/an, so یک is often used when introducing a singular countable noun.

If you omit it and just say آپارتمان, the phrase can sound less explicit or more general depending on context. یک آپارتمان clearly tells the listener you mean one apartment / an apartment.

نزدیک means near or close to.

Here, نزدیک مرکز شهر describes the apartment:

• یک آپارتمان نزدیک مرکز شهر = an apartment near the city center

There is also an important pronunciation point. In full pronunciation, Persian normally has ezafe links here, even though they are not written:

• âpârtemân-e nazdik-e markaz-e shahr

So a learner may not see the -e sounds in the script, but they are part of natural pronunciation.

This is a noun phrase linked by ezafe.

• مرکز = center
• شهر = city

Together:

• مرکزِ شهر = the center of the city = city center

In normal Persian spelling, the ezafe is usually not written, so you see مرکز شهر, but it is pronounced markaz-e shahr.

Yes, دیروز can move, but its position here is very natural.

This sentence uses a common order:

• subject
  • time expression
    • object
      • verb

So:

• من و خواهرم دیروز یک آپارتمان نزدیک مرکز شهر دیدیم

You could also say:

• دیروز من و خواهرم یک آپارتمان نزدیک مرکز شهر دیدیم

That is also fine. Persian time expressions are fairly flexible, but putting دیروز before the object and before the final verb is very common.

The sentence follows the basic Persian pattern SOV:

• Subject: من و خواهرم
• Time expression: دیروز
• Object: یک آپارتمان نزدیک مرکز شهر
• Verb: دیدیم

So the full structure is:

subject + time + object + verb

One of the most important habits for English speakers learning Persian is getting used to the verb coming at the end.