In english language, When Do i use "Other" and When do I use "Another"?

In THE English language, you use "another" when you already have one or more of something.  For example:  I have one cat and I want another so it has company.

You use "other" when there are two of something.  For example, when there are two screwdrivers:  This one is too small.  Hand me the other.

Basically, "other" means different, and "another" means more.  More, or less!

Another is singular, other is plural. The doctor had another patient to see. The doctor had other patients to see. The doctor had three other patients to see. 

Another is just the two words an other rolled into one. Of course you only use another where the indefinite article is called for, else it's the other. Two patients had appointments. One arrived on time. The other texted that he would be late.