Learn Hardcore Turkish: Çalar saat beni uyandırdı.

Çalar: Aorist 3rd person singular of çalmak (to ring/play/steal), used attributively to mean “that rings.”
saat: “clock.” Together çalar saat is the set phrase “alarm clock.”
beni: 1st person singular accusative pronoun, “me” as a direct object.
uyan-dır-dı: uyan- (wake up, intransitive) + causative -dır (make someone do) + past -dı (3sg). Overall: “(he/she/it) woke (someone) up.”

Why is it çalar saat and not something like çaldı saat?

Because çalar here is an attributive (adjectival) aorist meaning “that rings,” forming the noun phrase çalar saat “alarm clock.” Çaldı is a finite past-tense verb (“rang”), so çaldı saat would be ill-formed as a noun phrase; as a sentence, you’d say Saat çaldı (“The clock rang”).

Does Turkish mark “the” versus “a”? How do I know whether çalar saat is definite?

Turkish has no articles like “the” or “a.” Çalar saat can be interpreted as either “the alarm clock” or “an alarm clock,” depending on context. Definiteness for direct objects is often shown with accusative case, but subjects (like çalar saat here) don’t take case for definiteness; context does the job.

Why is beni in the accusative?