The old way to accomplish Exchange calendar sharing between users was to either connect to each individual users workstation to right click and share the calendar to users in the Global Access List (GAL) or to install their profile on your system and do the same. There have been some wonderful advances since the advent of Powershell that allow Office 365 calendar sharing permissions to be set remotely as follows:
Once this command has been executed for each individual recipient that will access the sharing users calendar, then you can have them right click to add the shared calendar in their Outlook. For a list of possible Access Rights see this great page by the University of Wisconsin. If your company is using Office 365 Calendar and needs help sharing them, then contact us for assistance.