How to write all pairwise test case manually?

I have been studying about all pair testing. And I see that tools do this.

But I want to know how to enumerate all cases such that all pairs are covered manually. What is the logic you follow to enumerate all cases. Please suggest a logic to do this.

There seems to be link in tutorial point, but it just asks to ensure that all cases are covered instead of saying how to do.

Can someone help ?