" ~ ni naru"
--- Michiko became a lawyer last year.
--- Mr. Yamada will become principal next year.
--- Tomoko became sick from fatigue.
--- Summer has not yet come.
In these sentences, the words, "bengoshi" "kouchou" "byouki" and "natsu" all express the resulting state. As for the forth example, the subject is omitted.
Nature's seasonal changes, such as it getting hotter and spring arriving, are described using "naru". For example, "natsu ni narimashita 夏になりました", which literally means, "it has become summer". The English expression would be "summer has come".
Change in state may be expressed not only by nouns, as seen in the examples above, but also by adjectives. When accompanied by adjectives, they take adverbial form. As for the I-adjective, replace the final "~ i" with "~ ku" to make the adverbial form.
Ookii 大きい (big) ---- ookiku (naru) 大きく(なる)
Atarashii 新しい (new) --- atarashiku (naru) 新しく(なる)
Atsui 暑い (hot) --- atsuku (naru) 暑く(なる)
Yasui 安い (cheap) --- yasuku (naru) 安く(なる)
As for Na-adjective, replace the final "~ na" with "~ ni".
Kireina きれいな (pretty) ---- kireini (naru) きれいに（なる）
Yuumeina 有名な (famous) --- yuumeini (naru) 有名に(なる)
Genkina 元気な (healthy) --- genkini (naru) 元気に(なる)
Shizukana 静かな (quiet) --- shizukani (naru) 静かに(なる)
Here are some examples with adjectives.
--- The puppy will become big quickly.
--- It has gotten warm, hasn't it?
--- The store has become very famous.
"~ you ni naru"
"~ you ni naru" usually indicates a gradual change. It can be translated as, "come to ~; it has come to be that ~; has finally become" etc.
--- Nancy is finally able to speak Japanese a little.
--- I've finally come to understand her feelings.
--- Hiroshi has come to eat everything well.
--- My father has reached the point where he doesn't drink sake.
--- I have come to read even the difficult kanji.
"You ni" by itself can be used as an adverbial phrase, along with other verbs (not just, "naru"). For example, "Kare wa nihongo o nihon jin no you ni hanasu 彼は日本語を日本人のように話す。 (He speaks Japanese like a Japanese person.)"
"~ koto ni naru"
While, "~ you ni naru" describes a shift or change, focusing on the result itself, "~ koto ni naru" is often used when someone's decision, or an arrangement, is involved. It translates to, "it will be decided that ~; come about ~; turn out that ~". Even if the speaker decides to do something, it sounds more indirect and more humble to use this structure rather than using, "koto ni suru (decide to do)".
--- It has been decided that the bank will employ me next month.
--- It's been arranged that I will get married next May.
---- In Japan, cars are supposed to be driven on the left side.
--- It's been arranged that I'm going to see Mr. Tanaka today.
--- It may turn out that Mike will teach English in Japan.
