- Launch Skype on your iPhone. You will be on one of the pages of Skype interface. 
Click Menu Button
- Click the menu button in the bottom left of any Skype page. A menu will pop up.
Click “Add People”
- In the pop-up menu, click “add people”. A searching field will appear.
Search for People to Add
- Enter the Skype name of the one you want to add in the searching field and tap “Search” in the bottom right of the keyboard.
Tap the Name
- After you search for the Skype name of the people you want to add, his or her name will appear on the screen. 
Tap “Send Contact Request”
- Tap “send contact request” to send your request.  Then you can wait for him or her to accept the request.