You use get to or grow to in front of another verb to say that someone gradually acquires a particular attitude. Grow to is more formal than get to.
I got to like the whole idea.
I grew to dislike working for the cinema.
You also use get to to say that someone gradually becomes aware of something, or gradually becomes acquainted with someone or something.
I got to realize it more as I grew older.
I got to know a few people.
In American English, if you get to do something, you have the opportunity to do it, and you do it.
I got to do a little work in Cuba.
I never got to ride in one again.
Get to is not usually used like this in British English.
\Useful english dictionary. 2012.