أريد أن أبدأ هذا الدرس الآن، لكنها متعبة.

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

• الآن: now
• يريد: to want
• أن: (subordinating particle)

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: