I don't like it very much
Here comes 2 possible understandings
1.I hate it very much.
2.Though I do not like it very much, I like it a little.
Which one is right?
Of course, the meaning of these simple(r) statements depend a lot on context.
However, "I don't like it very much" is typically used as a polite way of saying that you really don't like something.
So you could see an exchange that goes like this...
Husband: What do you think of this shirt? How does it fit?
Wife: I don't like it very much...maybe try that red one over there.
This doesn't have to mean that she hates it. But it certainly implies more than the literal meaning of slight dislike or even light like.
It's basically a nice way of saying that you don't like something. Similar to how "I don't think so" is a nice way of saying no to something like an invite (Q: Will you be coming to dinner tonight? A: I don't think so...sorry.)