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: 
Beyond the answers given by other contributors, I would also add another parse:

If asked at a bar at night, when the other party is clearly not drinking coffee, the individual who asked may be implying that they will be making coffee for the other party the following morning; that is, it could also serve as an implicit pick-up line.
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!
> 
> 
> 

(This is me. :))