Here are some examples for you.

Can I have another cake? Means I have eaten one cake and I want some more.

Are there any other cakes? Means I don't like this cake what else do you have?

He bought another car. Means he already has one car and he bought one more

He bought the other car. Means he was thinking about buying one car but he bought a different one instead.

I want to go to the party, the other kids are going. Means he is not going but his friends are.

There's another kid going to the party. Means one more kid is going to the party.

This is very similar to Rebecca's answer, but it might be useful in any case.

Contrast ‘the other’ with ‘another'

  I want the other dress - there is only one other dress, and you want it.

  I want another dress - there are many other dresses you can choose from

  Here is the other boy - there is only one other boy, and here he is

  Here is another boy - there are many other boys, here is one of them

Sometimes you use another when you want the same thing again:

  I want another drink. Generally means I want the same drink again.
  i want another coffee. Means I want the same coffee again.

If you want a second drink, but you want something different, then you have to be clear.

  I want another drink, something different.

Or if you do want the same again, you can make that clear to:

  I want another drink, the same again.

I’m sure there are many other uses of ‘other’ and ‘another’ that are confusing. Let me know if you have a specific example!

another is like asking one more thing, and other is asking different thing, i too learning English, if you get the correct answer means share with me friend.