Learn German: Warum regst du dich so über Politik auf? - Why do you get so upset about politics?

The verb here is sich aufregen (to get upset). It is a reflexive verb, meaning the action reflects back onto the subject. Because this verb requires the accusative case, the reflexive pronoun for du (you) is dich (yourself).

Why is the word auf sitting all by itself at the end of the sentence?

That is because the full verb is sich aufregen. It is a separable verb. In a main clause like this, the core verb (regst) takes the second position, and the prefix (auf) gets kicked to the very end of the sentence.

Why is the preposition über used to mean 'about'?

Many German verbs pair with specific prepositions that you just have to memorize. sich aufregen pairs with über to mean 'to get upset about' something. When used with this verb, über always triggers the accusative case.

Could I put dich somewhere else in the sentence, like after Politik?

No, the word order is strict here. In a question, the verb (regst) comes in position two, followed by the subject (du). The reflexive pronoun (dich) likes to stay as close to the subject as possible, so it must come immediately after du.