In Windows 10, once you are connected to the network you want to set to Private,
- Start a Windows Explorer window
- Click on “Network” among the items listed on the left of the window
- If you have disallowed sharing on Public Networks (recommended) and allowed on Private, there should appear a (yellow) warning in the upper part of the Explorer window to remind you that “Network discovery and file sharing is turned off. Network computers and devices are not visible. Click to change…”
- Click on the warning
- Respond appropriately to the new pop-up asking if you actually want to allow sharing on Public (NO), or change network to a Trusted/Private network.
- Select second option to change network to a Private/Trusted one.
Similar article for Windows 8.1: http://answers.microsoft.com/en-us/windows/forum/windows_7-networking/change-type-to-private/97993d60-58e0-4536-a31e-df89cccb7fe1?auth=1