I will have another coffee => means you have already had a coffee, but you want one more! I will have other coffee => means you don't like the cup of coffee I am offering you, for example, the cup is dirty or it is too sweet, so you ask me to prepare a different coffee for you.

Hi Kou, "Another" is simply the singular form of "other." "Another" is the English way of saying "one other" (we just combine "an other" into one word: "another"). The easiest way to remember this: is the object you're describing singular or plural? If it's singular, use "another"; if it's plural, use "other." For example: "I'll have another coffee." This means "I'll have one other coffee," not more than one. "I'll have other coffees." This means I'll have more than one other coffee. I hope this helps clarify some confusion. Please let me know if you have any more questions =)