We use another + a singular noun and other + a plural noun when both of them are used as determiners.
Example
- I need another cup of coffee. (singular)
 - I want to talk to other doctors. (plural)
 
When discussing the second of two things, or the opposite of two things, we use the other + a singular noun (observe that there is the before other),
Example
- This computer here is new.
 Anothercomputer is about five years old. ❌- The other computer is about five years old. ✅
 
Additionally, to refer to the remaining items in a group, we use the other + a plural noun.
Example
- Joel and Karen are here, but where are the other kids?
 
References