هذه أغنية جميلة.

In Arabic, the verb to be is usually not expressed in the present tense.

So:

• هذه أغنية جميلة literally looks like this beautiful song
• but it means This is a beautiful song

This is very normal in Arabic.
If you wanted was, then Arabic would use a verb, such as كانت.

هذه means this for a feminine singular noun.

Since أغنية (song) is feminine singular, Arabic uses:

• هذه = this (feminine)
• not هذا = this (masculine)

So the sentence begins with the demonstrative this, just like English does in This is a beautiful song.

In Arabic, nouns have grammatical gender: masculine or feminine.

أغنية is feminine. One clue is that it ends in ة (called taa marbuuTa), which very often marks a feminine noun.

So because أغنية is feminine:

• the demonstrative is هذه
• the adjective is جميلة

Everything agrees with the noun’s gender.

In Arabic, adjectives normally come after the noun they describe.

So:

• أغنية جميلة = a beautiful song

This is the normal Arabic order:

• noun + adjective

Also, the adjective must match the noun in:

• gender
• number
• definiteness
• case

So جميلة matches أغنية because both are feminine singular and indefinite here.

Because أغنية is feminine.

Arabic adjectives must agree with the noun they describe. Since أغنية is feminine singular, the adjective must also be feminine singular:

• جميل = beautiful (masculine)
• جميلة = beautiful (feminine)

So أغنية جميلة is correct.

Because the sentence means This is a beautiful song, not This is the beautiful song.

In Arabic:

• أغنية جميلة = a beautiful song (indefinite)
• الأغنية الجميلة = the beautiful song (definite)

When a noun is indefinite, its adjective is also indefinite.
So both words appear without ال.

Yes, but it means something different.

• هذه أغنية جميلة = This is a beautiful song
• هذه الأغنية جميلة = This song is beautiful

In the first sentence, أغنية جميلة is the description of what this is.
In the second, هذه الأغنية means this song, and جميلة is telling you something about it.

Both are correct, but they are not identical in meaning.

A common pronunciation is:

hādhihi ughniyatun jamīlatun

In normal pausal pronunciation, especially at the end of a sentence, you will often hear:

hādhihi ughniya jamīla

A rough guide:

• هذه = hā-dhi-hi
• أغنية = ugh-ni-ya
• جميلة = ja-mī-la

Notes:

• ذ sounds like th in this
• غ is a deep, throaty sound not found in English
• ج in Modern Standard Arabic is often taught as j as in judge

That letter is called taa marbuuTa (ة).

It often appears at the end of feminine nouns and adjectives. In this sentence:

• أغنية ends with ة
• جميلة ends with ة

When you pause, it usually sounds like -a:

• ughniya
• jamīla

But in full grammatical reading with case endings, it can sound like -tun:

• أغنيةٌ = ughniyatun
• جميلةٌ = jamīlatun

The mark أ at the beginning is an alif with hamza.

It shows that the word begins with a glottal stop, something like a brief catch in the throat before the vowel. So أغنية begins with a clear opening sound:

• ʾughniya

For a beginner, the main thing is simply to remember that the word starts with أ, not plain ا in spelling.

In fully vocalized, formal Arabic, the sentence is:

هٰذِهِ أُغْنِيَةٌ جَمِيلَةٌ

Those -un endings are part of case endings and tanwīn.

Here, both أغنيةٌ and جميلةٌ are indefinite and nominative.
In careful grammar terms, this is because they are part of a nominal sentence.

But in everyday reading, speaking, and most unvowelled text, learners often see and say:

• هذه أغنية جميلة

without pronouncing the final -un endings.

It is a demonstrative pronoun/determiner meaning this.

In beginner-friendly terms, it functions like English this.
It points to something nearby.

In هذه أغنية جميلة, هذه stands at the beginning of the sentence and introduces what you are talking about: this.

Sometimes Arabic allows different word orders, but for this exact meaning, هذه أغنية جميلة is the most natural basic form.

If you change the structure, the meaning or emphasis may change. For example:

• هذه أغنية جميلة = This is a beautiful song
• الأغنية جميلة = The song is beautiful

So while Arabic is flexible in some ways, beginners should learn this sentence as a standard pattern:

• demonstrative
• noun
• adjective

It is a nominal sentence in Arabic.

A simple way to understand it is:

• هذه = the topic, this
• أغنية جميلة = the information about it, a beautiful song

So the overall pattern is:

• this + noun phrase

More literally:

• this [is] a beautiful song

This is one of the most common and useful Arabic sentence patterns.