Summarize:

You can do this by clicking the Start menu (the Windows logo at the bottom-left corner of the screen) and selecting Skype from the apps list. If you haven’t yet signed in to Skype, enter your login details and click Sign In. You’ll find it under “Recent Conversations” in the left panel of Skype. If you don’t see the group in this area, you can search for it using the Search bar at the top of Skype. You’ll see it at the top of the conversation window. This displays a list of everyone in the group. This opens the persons profile. You’ll see it beneath the word “Skype” on the right side of their profile. You’ll need to type this exact username in a moment, so be sure to write it down if it’s hard to remember. You can do this by clicking the arrow at the top-left corner of the person’s profile. Replace “<username>” with the new admin’s Skype username. The person you selected is now a group admin.  You can view a list of all admins by clicking the group’s name at the top of the conversation. To add an additional group admin, repeat this process using another group member’s Skype name.
Open Skype. Select the group chat. Click the list of participants. Select the person you want to make an admin. Find the person’s Skype username. Return to the group chat. Type /setrole <username> MASTER. Press ↵ Enter.