This determiner is ... well, in singular form, it's the second word in the first paragraph. Another.
When used with an uncountable or plural noun, it's other.
Another is actually an other, put together to form one word. Since we can only use an (which basically means one) with singular countable nouns, we can only use another with the same group.
I'll have another glass of beer.
She's not talking about The Sun Also Rises. She's talking about another book.
The problem usually appears when we use an uncountable or plural noun, in which case the word is not another, but other.
We need to find other sources for our raw materials.
Laura is relying on other information.
Let's try some other restaurants next month.
Note that for plurals, and sometimes for uncountables, we can use some other instead of just other alone. We can also use a few other, several other, etc.
Next time, we'll look at the difference between other and different.