هذا يوم جميل، وأنا أريد أن أذهب إلى المدينة.

هذا is the masculine singular demonstrative this. It matches the gender of يوم (day), which is grammatically masculine in Arabic.
If the noun were feminine (e.g., مدينة), you’d use هذه: هذه مدينة جميلة (This is a beautiful city).

Yes. In Modern Standard Arabic, the present tense to be is usually not stated. A nominal sentence like هذا يوم جميل literally looks like This (is) a beautiful day.
If you want to express was or will be, Arabic typically uses كان (was) or سيكون (will be).

In Arabic, adjectives normally come after the noun they describe. Also, the adjective must agree with the noun in:

• gender (masculine/feminine)
• number (singular/dual/plural)
• case (nominative/accusative/genitive)
• definiteness (definite/indefinite)

Here, يوم is masculine singular and indefinite, so the adjective is جميلٌ (often written without the final vowel in everyday text).

و means and and is commonly used to link clauses. The comma is just punctuation, not a grammatical requirement.
So ...، وأنا ... is ..., and I .... You could also write it without the comma in some styles.

Often you don’t need أنا, because the verb form can show the subject. أريد already means I want.
But أنا can be used for emphasis or clarity, especially when contrasting or highlighting the subject: وأنا أريد... = and I (for my part) want...

The verb أريد comes from the root related to wanting (أراد). In the present tense, أ- at the beginning is the marker for I in many verb patterns.
So:

• أريد = I want
• تريد = you (m.) want / she wants (context decides)
• يريد = he wants
• نريد = we want

أن is a particle that often means to when one verb is followed by another verb (a “verbal noun” / subordinate clause):
أريد أن أذهب = I want to go (literally: I want that I go).
After أن, the following verb is typically in the subjunctive (often not visibly marked in unvowelled text).

أذهب is I go (present tense). Depending on context, it can mean I go or I am going.
Arabic can also use other verbs for specific nuances, like أغادر for I leave/depart.

إلى means to/toward (movement or direction): أذهب إلى المدينة = I go to the city.
لـ often means for/to (as in “for someone” or “belonging to”) and is used differently, e.g., هذا للطالب (This is for the student).

المدينة means the city. Arabic often uses the when the destination is understood as a specific city (from context) or when speaking generically about “the city” as a known place (like “downtown”).
If you want a city, you’d typically say إلى مدينةٍ (often written إلى مدينة without vowel marks).

The conjunction و is usually pronounced wa- and attaches to the next word: وَأنا (wa-ana).
In fast or connected speech, the vowel can sound lighter, but in MSA reading it’s typically wa.

They’re usually not written in normal Arabic text, but they exist in fully vowelled MSA. In careful MSA, you might see something like:

• هذا يومٌ جميلٌ، وأنا أريدُ أن أذهبَ إلى المدينةِ.

In everyday reading/writing, most people rely on context and don’t include these vowel marks.