how remind a professor we were supposed to have a conversation through Skype?
This is a starting point.  You can adapt this to your own style.

Dear Prof. X,
I hope all is well with you.  Did I misunderstand when our Skype appointment is?  I thought it was yesterday.  Maybe I should make sure I know what your skype ID is.  Is it profx?  Mine is maryam.
If you have time next week -- days that would work for me are m, n, or p.
I'm attaching my unofficial transcript.
Sincerely,
(name)