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: 
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.
It's easier to see the meaning if you expand the two sentences to avoid the ambiguity:

> 
> How do you like your coffee [to be]?
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> 
> 

And the second definition:

> 
> How do you like your coffee [in front of you]?
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> 

---

The latter is usually instead said without the "how" (in fact, I have a feeling including the "how" is grammatically incorrect), just as:

> 
> *Do you like your coffee?*
> 
> 
> 

Or even more clear: 

> 
> *How is your coffee?*
> 
> 
>