Microsoft has an article on how to do this as well, in case this is not exactly what you need: https://support.office.com/en-us/article/Share-a-contacts-folder-with-others-ce5a40d1-bc9f-4f5d-a2aa-5ec388573821?ui=en-US&rs=en-US&ad=US
Sharing a folder, including a local contacts group, is a two-step process.
Step One: right-click the folder in Outlook and choose Properties.