@WBYeats,
My (Korean) students also have a problem with this, due to the fact that Korean language has the same word for both actions (찾다). This is how I explain the difference between 'finding' and 'looking for':
When you find something, it's a momentary event. When you were looking for it, that took a longer time.
Ex:
I lost my pen. I was looking for it for 15 minutes. (long action)
Then I found it. (short action)
I've been looking for a job for a month. (long time) Yesterday, I found one. (short time)