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: 
As the other answers suggest, `"How do you like your coffee?"` can indeed have either meaning, depending on context.

If you're looking for unambiguous versions, you could instead ask:

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> How do you take your coffee? `Meaning: Milk? Sugar?` 
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Or

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> How is your coffee? `Meaning: Do you like the coffee you're drinking?`
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It's easier to see the meaning if you expand the two sentences to avoid the ambiguity:

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> How do you like your coffee [to be]?
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And the second definition:

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> 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:

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> *Do you like your coffee?*
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Or even more clear: 

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> *How is your coffee?*
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