Hello Nancy, it usually doesn't really matter. As a teacher I normally send the student a contact request first of all (so we can use the chat box) But some students contact me. It may also be that your Skype address as shown on Skype is not correct. If you are talking about instant lessons then if you have waited more than 5 minutes and not been contacted by the teacher (on Skype or Italki) then I would initiate contact.
Best wishes
Bob