From the Calendar in Outlook click the down arrow on the Share Calendar button then click the Calendar option under your email address:
From the Permissions tab in the Calendar Properties Dialogue box click the Add... button. You have the option in this window to set their permissions, in the bottom Permissions box.
Type the surname of the person you would like to give permissions for your calendar and click the arrow next to their name, either double click on their name or click the Add button at the bottom, you can add several names at the same time. Then click the OK button for the Add Users dialogue box.
Then select the level of permissions you would like to give the person, Can edit allows them to view, add and delete appointments on your calendar. Delegate allows them to schedule, accept and respond to calendar invites on your behalf. After selecting which level, click Apply.
That person will receive an email from you advising they would like to share their calendar with you, click the Apply button at the top left hand corner of the email. You should be able to see their Calendar and edit if you allowed that setting.