From New Zealand 2007年7月，ニュージーランドへ移住してきました。ニュージーランドでの日常生活についてつづります。

Surprised by something
= something jumped out of the bushes as scared the pooh out of me.
'Surprised by' refers to an emotional response, eg. "I was surprised by his lack of initiative."


Surprised at something
= I noticed/learned something which surprised me to learn.
'Surprised at' refers to an intellectual response, eg. "I was surprised at his lack of initiative."

In both cases, 'something surprised me' works, eg. "His lack of initiative surprised me."
Here, the listener is unsure whether the speaker means he was emotionally surprised or intellectually surprised.
'I was surprised' works, but the listener obviously needs to know the context.