Question: > 
> How do you like your coffee?
> 
> 
> 

Can I use the above sentence either on an offering situation that I ask if they like it black or with sugar, or during having situation that I ask if the coffee tastes good?

When the latter is possible, can next both answers be possible? 

1. I like it a lot.
2. It's good.

Answer: 
This phrase does have two meanings in US English, as agreed by other posters.

For the sake of completeness, I feel compelled to add that in British English, this is a phrase that would only be used when offering coffee. Using it as a question to affirm how much someone was enjoying their coffee would probably be understood, but would sound extremely odd. Instead, British people might say:

> 
> "Are you enjoying your coffee?"
> 
> 
> "Is that coffee OK for you?"
> 
> 
> 

Or something similar.

Divided by a common language and all that.
Good question -- in addition to the answers concerned with the various contexts in which this is asked:

The ambiguity is as much a question of contrastive focus:

* **How** do you like your coffee?
* How **do** you like your coffee?
* How do **you** like your coffee?
* How do you **like** your coffee?
* How do you like **your** coffee?
* How do you like your **coffee**?

Even context-free, emphasis on the words in bold (or any combination of words in this sentence) affects the meaning. See [Wikipedia: Focus (linguistics)](http://en.wikipedia.org/wiki/Focus_(linguistics)) for a more technical description of contrastive focus.