This document describes how internet connection sharing (ICS) can be enabled on Windows 10 IoT Core. Developers can use the NetworkTetheringManager API to configure ICS programmatically. The API is described in the NetworkOperatorTetheringManager class. When using one of the Windows 10 IoT Core Release Image ICS can also be configured using the device portal.
See Windows Device Portal (WDP).
The code sample below demonstrates how the NetworkOperatorTetheringManager API is used to start sharing an Ethernet connection over Wi-Fi. The CreateFromConnectionProfile method accepts arguments that specifies the public and private interface. In any cases of misconfiguration, such as the Wi-Fi radio is turned off, or Ethernet has limited connectivity, then the attempt to start internet sharing conveys an appropriate error code pertaining to this scenario.
If you using the Windows IoT Core November 2015 Release you need to follow the instructions described in the Internet Connection Sharing Tutorial (Windows IoT Core November 2015 Release) document.