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Tap the Skype app icon, which resembles a white "S" on a blue background. If you aren't logged into Skype, you'll need to enter your email address (or phone number) and password before continuing. It's a person-shaped icon at the top of the screen. Doing so opens a list of your contacts. This option is at the bottom of the screen. Tapping it prompts a menu to open. It's in the menu. This opens a text box. Doing so searches Skype for your specified contact. Tap the name of a contact whom you want to add. It's a blue button in the middle of the page. This option is below the text box. Doing so sends an invitation for the person to join your contacts; if they accept, you'll see them online, and you'll be able to chat with them as you please. You can first edit the invitation message by typing your preferred message into the text box that appears. If your friend doesn't already have a Skype account, you can invite them to create one and join you on Skype by doing the following:  Tap the "Contacts" icon in the bottom-right. Tap Invite People to Skype. Select a contact method (e.g., your text messaging app or Gmail). Enter your friend's contact information (e.g., their phone number or email address). Tap the Send button or icon.
Open Skype. Tap the "Contacts" icon. Tap ＋. Tap Find people. Enter a name, email address, or phone number. Select a result. Tap Add to contacts. Tap Send. Invite a friend to join Skype.