Learn Russian: Я оставил тебе записку на столе.

You use the perfective aspect here because you are talking about a single, completed action that has a current result. The focus is on the fact that the note is now on the table, not on the ongoing process or habit of leaving it.

Why is the pronoun тебе in the dative case?

The dative case is used for the indirect object, which is the person receiving something. Since you are leaving the note for or to them, the base pronoun ты changes to тебе.

Why does the word for note change from записка to записку?

Записка is a feminine noun ending in -а. Because it is the direct object of the verb (the actual thing being left), it takes the accusative case, which changes the -а ending to -у.

Since I am putting the note onto the table, why is на столе in the prepositional case instead of the accusative?

Even though placing a note involves motion, the verb оставить (to leave) focuses on the location where the item remains. It answers the static question where? (где?), rather than the motion question to where? (куда?). Therefore, стол takes the prepositional case and becomes столе.