Skype Only Hears One Way

Simple Solutions
If you cannot hear the other person, check to make sure the audio on your computer is turned on. Check your speakers, if you have them, to make sure they are not turned down or off. If your contact cannot hear you, suggest that she check these things on her computer. The party who can't receive sound should also check the volume settings in Skype within the call. Click the small 'Volume' icon at the bottom of the call screen to adjust your volume in Skype. If you cannot hear her, ask her to check her microphone (if applicable) to make sure she did not accidentally press 'Mute' or a similar button. Try the same thing if she cannot hear you.
Test Call
Both of you should make a Skype test call to help determine where the problem lies. Find the contact named 'Skype Test Call,' 'Echo/Sound Test Service,' or something similar in your contact list. Call this contact. This plays a recording asking you to record a message. Do so. You should then hear your message played back to you. If you do not hear anything, the problem may lie with your speakers or your audio equipment. Once you and your friend have both done this, you can figure out exactly where the problem lies and focus on resolving it.
Call Quality Settings
Check your call quality settings and ask your contact to do the same. Clicking the 'Check settings' button in any Skype chat window gives you information about the status of various equipment, such as your microphone, your speakers and your webcam. If there is a problem with any of these, or if you have a poor connection (as shown in the connection tab), you know where to focus your attention. You can test your microphone, speakers and connection from within the window that opens when you click 'Check settings.'
Update Skype
If nothing else seems to work, both of you should try updating Skype to the latest version. The problem may be a known glitch that has been resolved with updates. To update Skype, click 'Help' and then 'Check for Updates' from within Skype. If an update is available, follow the prompts to update the program. You may need to restart Skype. Do so, and then attempt to make your call again.