Question: > 
> How do you like your coffee?
> 
> 
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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: 
**Be careful of emphasis**

There are 2 ways of emphasizing the question:

1. *How* do you like your coffee?
2. How do you like *your coffee*?

The first is equivalent to 'how do you take your coffee?', so I would expect it in that context after someone has agreed to or requested some coffee.

The second is equivalent to 'how are you enjoying your coffee?', so I would expect it in the context of someone having tasted some coffee they have received. To this, any answer about the quality or my enjoyment of the coffee is fine, but it is not a yes/no question ('how' requires a full answer).
One other possible interpretation is if it's being said by someone who doesn't like coffee, in an incredulous manner:

> 
> *How* do you like your coffee?? I hate it!
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> 
> 

(This is me. :))