أريد أن أبدأ هذا الدرس الآن، لكنها متعبة.

I want to start this lesson now, but she is tired.

Breakdown of أريد أن أبدأ هذا الدرس الآن، لكنها متعبة.

• هذا: this
• الآن: now
• يريد: to want
• أن: (subordinating particle)
• متعب: tired
• الدرس: lesson
• يبدأ: to start
• لكنها: but she

Questions & Answers about أريد أن أبدأ هذا الدرس الآن، لكنها متعبة.

Why is أريد translated as I want even though there is no word for I?

Arabic verbs encode the subject in the verb form itself. أريدُ is the 1st person singular (I) form of the verb أرادَ (to want), so it already means I want without needing أنا.
You can add أنا for emphasis: أنا أريد أن أبدأ... (I (specifically) want to start...)

What is the function of أن before أبدأ?

أن here means to in the sense of an infinitive-like clause: I want to start.
Grammatically, أن introduces a subordinate verb clause and typically puts the following imperfect verb into the subjunctive mood.

Should أبدأ have a different ending after أن?

Yes—in fully vowelled Arabic, after أن the verb is normally subjunctive (منصوب), so it would be written/pronounced أبدأَ (final -a).
In most everyday writing, those final vowels aren’t shown, so you just see أبدأ.

Why does the sentence say هذا الدرس and not هذا درس?

Both are possible, but they’re slightly different:

• هذا درس = This is a lesson / This is (a) lesson (more like introducing it as a lesson).
• هذا الدرس = this lesson / this specific lesson (more definite and specific).

Using the definite article الـ with the demonstrative is very common when you mean a specific known item.

Why is it هذا and not هذه?

Demonstratives agree with the noun’s grammatical gender:

• درس is masculine, so you use هذا.
• هذه is used with feminine nouns (e.g., هذه الصفحة = this page).

Where would the object case ending go (if we added diacritics)?

In fully vowelled MSA, هذا الدرس is the object of أبدأ (I start this lesson), so الدرس would typically be accusative (منصوب):

• أريدُ أن أبدأَ هذا الدرسَ الآنَ
  Again, these final vowels (-a) are usually omitted in normal writing.

Is الآن placed correctly? Can it move?

Yes, الآن (now) is natural at the end. It can also move for emphasis or style:

• أريد أن أبدأ هذا الدرس الآن (very common)
• الآن أريد أن أبدأ هذا الدرس (Now, I want to start this lesson)

All are understandable; end position is often the most neutral.

What exactly is لكنها and why is it written as one word?

لكنها = لكنّ (but) + ها (her / it [feminine]) as an attached pronoun. Arabic commonly attaches object/possessive pronouns to words like this.
In careful MSA, it’s often written with a shadda: لكنّها.

Why is it لكنها and not لكن هي?

Both exist, but they differ in structure and emphasis:

• لكنّها متعبة = but she is tired (a standard, compact MSA structure)
• لكن هي متعبة = closer to but she (in particular) is tired; it can sound more contrastive/emphatic and is less “textbook-formal” than لكنّها in strict MSA.

Who does ها refer to? The sentence mentions الدرس—could it mean but it is tiring?

As written, ها is feminine, so it most naturally refers to a feminine person already understood in context (e.g., a female teacher/student).
It is unlikely to refer to الدرس because درس is masculine; but it (the lesson) is tiring would normally be:

• ... لكنه متعب (masculine هو/ـه)
  If you meant but it is tiring referring to a feminine noun (like الحصة “the session/class” feminine), then لكنها متعبة would fit.

Why is متعبة feminine, and what changes if the subject is masculine?

متعبة is a feminine singular adjective meaning tired (or tiring depending on context, but here it’s most naturally “tired”).
Adjectives agree with the noun/pronoun they describe:

• feminine: هي متعبة / لكنها متعبة
• masculine: هو متعب / لكنه متعب

How do you pronounce the final ـة in متعبة?

The final ـة (taa marbuuTa) is usually pronounced:

• as -a / -ah in pause: mutaʿbah
• as -t if followed closely by another word in connected speech (especially in formal recitation): mutaʿbatun (with case ending) or mutaʿbat… depending on grammar.
  In normal spoken reading without case endings, you’ll most often hear mutaʿbah.

Is the comma necessary in Arabic? How is punctuation handled here?

The comma isn’t grammatically required, but it’s often used in modern writing to reflect a pause, especially before contrast like لكنّ....
You may also see the Arabic comma ، instead of the English comma:
أريد أن أبدأ هذا الدرس الآن، لكنها متعبة.