I''m a Chinese learner for quite a while, I've been wondering why (是) shi4 is dropped in sentences like this："我很好" Isn't there supposed to be a verb in every sentences? like 我（是）很好.
Simply put, adjectives in Chinese can function as verbs.
You can refer to the answers of this previous question for more details: Stative verbs in Chinese: only for adjectives?
Generally speaking, “是” means “is”. In English you can use "be"+adjective to mean "A subject whose property/attribute is of sth"：
But in Chinese, “是” is usually means "to define a subject to be sth"：So when we say "some subject" “是” "sth", this means "Some subject equals sth".
我是学生：I'm a student (meaning I'm working as a student). So “是” is usually used with a noun.
However, “是” can be also used to enhance a meaning (just like your example above)——this means some subject is REALLY sth, maybe according to the context, this is something with your mood.
我是很好！(Of course I'm fine, maybe someone is saying badly about you.)
他是很坏！(He's really very bad, agreeing with sb's saying)
是 is a contact verb here.