Skype needs to connect to the Internet to verify account information, and generate encryption keys. The Skype network is created by all of its users; it's a peer-to-peer network. Every computer connected acts as a client and a server. Once a Skype account authenticates online it can operate within your LAN. Since Skype uses the fastest connections available to it, it will remain within your LAN as long as all the users it's communicating with are within that LAN.
Connect to your LAN, and have all your Skype contacts do the same.
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Start Skype, and log in to your account. Have all contacts you wish to communicate with do the same.
Start a chat, audio call or video call with another Skype user in your LAN. The communication will take place over your LAN.