"There are many trees on top of the mountain."
It was taught to me like this. If it can't get up and leave by itself, we use ある. If it's capable of moving (from place to place without the aid of something else) it's いる.
Rocks, grass, trees, notebooks, and clocks are ある. While cats, dogs, people, and elephants are いる.
Now here's where it gets tricky. Apparently fish in a stream can be いる but fish in a pet store are ある.
Also, a bus by itself is いる. But a bus being driven by a man is ある. It's really confusing.
Normally, Kanji have 2 readings, the chinese reading (onyomi) and the japenese reading (kunyomi). The kanji 木's onyomi is moku and the kunyomi is ki. In general, the japenese reading is used when the kanji is used on its own like in tree (ki 木). The onyomi is used in compounds like thursday (mokuyoubi 木曜日)
Note that i am note a native japenese speaker, so take the things above with a grain of salt.