في عطلة نهاية الاسبوع اذهب الى السوق مع امي، ثم اعود الى البيت قبل الغداء.

This is a very natural word order in Arabic. A time expression often comes first to set the scene.

So:

في عطلة نهاية الأسبوع أذهب إلى السوق...

means something like:

On the weekend, I go to the market...

You could also say:

أذهب إلى السوق مع أمي في عطلة نهاية الأسبوع

and that is still correct. Starting with the time phrase just makes the time frame the first thing the listener hears.

Because the verb already shows the subject.

• أذهب = I go
• أعود = I return

In MSA, the prefix أـ on these present-tense verbs marks first person singular. So أنا is not necessary.

You can add أنا for emphasis:

أنا أذهب إلى السوق...

But in a normal sentence, Arabic usually leaves it out because the verb already tells you who is doing the action.

In Arabic, the present tense often covers:

• present actions
• habitual actions
• general routines
• sometimes near future, depending on context

Here, في عطلة نهاية الأسبوع makes it clear that this is a routine or habit. So:

أذهب = I go / I عادةً go أعود = I return / I come back

A native English speaker may expect something like I usually go, but Arabic often does not need a separate word like usually if the time expression already makes the habitual meaning clear.

It is an iḍāfa construction, often called a possessive or noun-link structure.

Breakdown:

• عطلة = holiday / break
• نهاية = end
• الأسبوع = the week

Together:

• نهاية الأسبوع = the end of the week
• عطلة نهاية الأسبوع = the weekend holiday / weekend

So the phrase literally builds up as the holiday of the end of the week.

A useful thing to notice: in an iḍāfa, the last noun often carries the الـ that makes the whole phrase definite. So نهاية الأسبوع is definite because الأسبوع is definite, and then عطلة نهاية الأسبوع is understood as a specific, known period: the weekend.

إلى means to and is used for movement toward a destination.

So:

• أذهب إلى السوق = I go to the market
• أعود إلى البيت = I return to the house/home

This is very similar to English to.

A helpful contrast:

• في السوق = in the market
• إلى السوق = to the market

So في is for location, while إلى is for direction or destination.

مع means with.

So:

• مع أمي = with my mother

The word أمي breaks down like this:

• أم = mother
• -ي = my

So أمي literally means my mother.

Because it comes after the preposition مع, it is part of a prepositional phrase: with my mother.

ثم means then, and it shows sequence more clearly than و.

So:

• ثم أعود إلى البيت = then I return home

If you used و instead:

• وأعود إلى البيت

that would simply mean and I return home. It still works, but ثم is better when you want to show that one action happens after another in a clear order.

Very roughly:

• و = and
• ثم = then / and then

Also, ثم often suggests a slight separation in time between the two actions.

In Arabic, البيت often means the house or home, and it is very common to use the definite form when talking about going home.

So:

• أعود إلى البيت literally = I return to the house
• natural English meaning = I return home

Arabic often uses the definite article where English may not. This is something learners have to get used to.

So even though English prefers home without the, Arabic very naturally says إلى البيت.

قبل means before, so:

• قبل الغداء = before lunch

Arabic very often uses the definite article with meals and other familiar daily events:

• الفطور = breakfast
• الغداء = lunch
• العشاء = dinner

So even though English says before lunch without the, Arabic commonly says قبل الغداء with الـ.

This is normal Arabic usage, not a special exception in this sentence.

In careful standard MSA spelling, those words are usually written with hamza.

So the standard spellings are:

• أذهب not اذهب
• أعود not اعود
• إلى not الى
• أمي not امي
• الأسبوع not الاسبوع

The sentence as written is understandable, and many people omit hamzas in fast informal typing. But if you are learning Modern Standard Arabic, it is better to learn the standard spellings:

في عطلة نهاية الأسبوع أذهب إلى السوق مع أمي، ثم أعود إلى البيت قبل الغداء.

A careful fully vocalized version would be:

في عطلةِ نهايةِ الأسبوعِ أذهبُ إلى السوقِ مع أمي، ثم أعودُ إلى البيتِ قبلَ الغداءِ.

A few useful things to notice:

• after في, the noun is genitive: عطلةِ
• in the iḍāfa chain, نهايةِ الأسبوعِ is also genitive
• after إلى, you get السوقِ and البيتِ
• the verbs in formal MSA end in ـُ: أذهبُ, أعودُ
• قبلَ is usually treated as an adverbial noun here, so it takes fatḥa
• the noun after قبل is genitive: الغداءِ

In normal reading and everyday writing, those short vowel endings are usually not written, but it is useful to know they are there in formal grammar.