في الصباح أغسل وجهي ويدي بالصابون، ثم أنظر في المرآة.

Because the verb form already tells you the subject.

• أغسل = I wash
• أنظر = I look

In Arabic, subject pronouns are often omitted when the verb already makes them clear. You can add أنا for emphasis, but it is not necessary.

In Arabic, the present/imperfect tense is used not only for actions happening right now, but also for habits and routines.

So in a sentence about a morning routine, أغسل and أنظر mean something like:

• I wash
• I look

in the sense of this is what I do.

في means in, and الصباح means the morning. So في الصباح literally means in the morning.

This is a very normal Arabic time expression. Arabic often uses a preposition like في with times of day.

You may also see صباحًا, which can also mean in the morning / mornings, but في الصباح is a very straightforward and common structure.

Because Arabic commonly says في الصباح for in the morning.

This is similar to English, where we also often say in the morning, not just in morning. The definite article here is natural and idiomatic.

Because Arabic attaches possessive pronouns directly to nouns.

• وجه = face

• وجهي = my face

• يد = hand
• يدي = my hand

The ending ـي means my.

So instead of using a separate word for my, Arabic usually attaches it to the noun itself.

That is just how possession normally works in Arabic. Instead of saying something like hand my, Arabic uses a suffix:

• يدي = my hand
• كتابي = my book
• بيتي = my house

This is one of the most basic and important patterns in Arabic.

As written, يدي means my hand.

If you want my two hands in correct Modern Standard Arabic, you would usually use the dual:

• يديَّ in the accusative/genitive
• يداي in the nominative

Since أغسل takes a direct object here, you would expect:

• أغسل وجهي ويديَّ = I wash my face and my two hands

So the sentence you were given literally says my face and my hand. If the intended meaning is my hands, the dual form would be the more standard MSA choice.

Here بـ means with or by means of. It shows the instrument or means used to do the action.

So:

• بالصابون = with soap

This is very common in Arabic:

• أكتب بالقلم = I write with a pen
• أقطع بالسكين = I cut with a knife

Because the noun appears here with the definite article ال:

• الصابون = the soap / soap

When بـ is attached to ال, they combine in writing:

• بِ + الصابون = بالصابون

Arabic often uses the definite article in generic expressions where English would simply say soap, water, bread, and so on. So بالصابون naturally means with soap.

Also, because ص is a sun letter, the l sound of ال is not pronounced. So it is pronounced approximately biṣ-ṣābūn, not bil-ṣābūn.

ثم means then and shows sequence.

So the sentence is saying:

1. first, I wash
2. then, I look in the mirror

Compared with other connectors:

• و = and
• فـ = so / then, often with immediacy
• ثم = then, after that

So ثم is a good choice when you want to show a later step in a routine.

Both expressions are possible, but they are slightly different.

• نظر إلى = to look at / toward
• نظر في = to look in / into, and sometimes to examine

With a mirror, في المرآة is very natural because you are looking in the mirror, meaning at your reflection.

So:

• أنظر في المرآة = I look in the mirror / into the mirror

If you said أنظر إلى المرآة, that would sound more like I look at the mirror as an object.

A fully vocalized version would be:

فِي الصَّبَاحِ أَغْسِلُ وَجْهِي وَيَدِي بِالصَّابُونِ، ثُمَّ أَنْظُرُ فِي الْمِرْآةِ.

A few useful points:

• في makes the following noun genitive, so:
  • الصَّباحِ
  • الْمِرْآةِ
• بـ also makes the following noun genitive:
  • بِالصَّابُونِ
• وجهي and يدي are the direct objects of أغسل, even though their case ending is not obvious because of the attached possessive ـي.

In normal everyday Arabic writing, these short vowels are usually omitted, so learners are expected to recognize the grammar from context.