
sich ärgern über
to get annoyed
To be angry or annoyed about a person, thing, or situation.
Ich ärgere mich jeden Morgen über den dichten Verkehr auf dem Weg zur Arbeit.
I get annoyed every morning about the heavy traffic on the way to work.
to annoy / to get annoyed
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to get annoyed
To be angry or annoyed about a person, thing, or situation.
Ich ärgere mich jeden Morgen über den dichten Verkehr auf dem Weg zur Arbeit.
I get annoyed every morning about the heavy traffic on the way to work.

to annoy
To deliberately annoy, provoke, or tease someone.
Mein kleiner Bruder liebt es, mich zu ärgern, indem er meine Sachen versteckt.
My little brother loves to annoy me by hiding my things.
Pay attention to the difference: 'sich ärgern' (to get annoyed) is reflexive and means that you yourself are angry. 'Jemanden ärgern' (to annoy someone) is transitive and means that you deliberately make another person angry.
Ich ärgere mich über das schlechte Wetter.
I get annoyed about the bad weather.
The verb 'ärgern' (to annoy / to get annoyed) is closely related to the noun 'der Ärger' (anger, trouble, annoyance). When you get annoyed, you have Ärger. When you annoy someone, you cause them Ärger.
Bitte mach mir keinen Ärger!
Please don't cause me any trouble!
When saying what you are angry about, you always use the reflexive form 'sich ärgern' (to get annoyed) with the preposition 'über' followed by the accusative.
Sie ärgert sich über ihren lauten Nachbarn.
She gets annoyed about her noisy neighbor.
When you deliberately provoke someone, you use 'ärgern' (to annoy) with a direct object in the accusative. This object is the person who is being annoyed.
Hör auf, deine kleine Schwester zu ärgern!
Stop annoying your little sister!
to upset / excite
Both sich ärgern and sich aufregen can describe a negative reaction to something disturbing. Sich ärgern focuses mainly on the annoyance or anger, while sich aufregen emphasizes more strongly that someone is emotionally agitated. Sich aufregen is therefore often more appropriate in cases of intense agitation.

Über die kurze Verspätung ärgerte sich Jana.
Jana was annoyed about the short delay.
Über den stundenlangen Zugausfall regte sich Jana sehr auf.
Jana got very upset about the train cancellation that lasted for hours.