You rarely use this phrase when talking about yourself. For example you wouldn't say "I want to get his goat." because it would sound stupid. You could say something like "He just want's to get your goat." or "It really get's my goat when that happens.". Remember, though, this is a very old phrase and if you used it now you would probably look silly. Try something more along the lines of "That really tics me off." or "That bugs me.". Those sound more modern and you'll look better saying it.

Get one's goat Meaning: To irritate or annoy someone. Examples: He really gets my goat when he makes fun of me like that. When people throw rubbish on the street it really gets my goat. Does anyone in your office get your goat? Example Dialogue: A: What's the matter? You look angry! B: Yes, I am a little. A: Why? B: George promised me the report would be finished by 3pm today. A: Is he late again? B: Yes, it really gets my goat when he does that.