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Open Skype. Click the "Contacts" icon. Click the search bar. Enter a name, email address, or phone number. Select a contact. Click Add to Contacts. Click Send. Invite a friend to join Skype.

Article:
Click or double-click the Skype app icon, which resembles a white "S" on a blue background. If you aren't signed into your Skype account, enter your email address (or phone number) and password to log in. It's a person-shaped icon in the top-left corner of the Skype window. This is the text box at the top of the Contacts window. Doing so will search Skype for your specified contact. Click the profile of a person whom you want to invite to be your contact. It's in the middle of the page. Doing so opens a window with a message in it. This is at the bottom of the window. Doing so sends a Skype invitation to the person; if they accept the invitation, you'll be able to chat with them. 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:  Click the "Contacts" icon. Click Invite People to Skype. Click Invite via email. Enter the email address of the person you want to invite in the "To" line. Click the paper airplane icon.