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You will be presented with your contact lists. Select the list that you want to add the contact to. This is located in the top right corner of the screen and looks like a silhouette with a "+" next to it. You can "Search Skype Directory", "Save a Phone Number", or "Import from iPhone". "Search Skype Directory" allows you to search for users by their name, Skype username, or email address. You will be presented with a list of search results after you enter your search. Tap the result that you want to add and then click the "Add Contact" button. You will be given the opportunity to customize the invitation text. "Save a Phone Number" allows you to enter someone's name and phone number and then add them to your contacts list. You can then call them using your Skype credits. "Import from iPhone" allows you to import your contacts from your iPhone and add their numbers to your Skype contacts. This will only add names and phone numbers, and will not add the person as a Skype user.
Tap the People button. Tap the "Add contact" button. Choose to your method.