This is the 2762nd most frequent Japanese word.
見つける
"To find" or "to discover."
In this sentence, '見つけました' is the past polite form of '見つける', and it denotes the achievement of finding or discovering something.
私は新しい本屋を見つけました。
I found a new bookstore.
Here, '見つけようとしています' indicates an ongoing attempt to find something, showing intent and action.
彼は鍵を見つけようとしています。
He is trying to find his keys.
In this sentence, '見つけた' is the past informal form, and it relates to discovering an item of interest in the past.