Tap the Skype app icon, which resembles a white "S" on a blue background. Doing so opens Skype if you're logged in. If you aren't logged in, enter your Skype email address (or username, or phone number) and password when prompted before continuing. Once the person begins calling you, your iPhone's screen will change to display the name of the caller at the top of the screen and answering options at the bottom of the screen. At the top of the screen, you'll see "Skype Audio" if the caller is using audio and "Skype Video" if the caller is using video. This tells you which type of call you'll participate in if you accept the call. If the contact is calling with video and you don't want to answer with video, you'll have to tap Decline and then call the contact back by tapping the phone-shaped "Audio" button in the upper-right corner of their conversation page. It's a white checkmark on a blue circle in the bottom-right corner of the screen. It may take a few seconds before you can hear (or see) the caller.
Open Skype. Wait for the Skype call to come in. Check the type of call. Tap Accept. Allow the call to connect.