To give an user (USER2) permissions to a different user's (USER1) calendar / contacts etc. run the following PowerShell commands on the Exchange server:

Firstly check the existing permissions for USER1's contacts & calendar folders:
(we're showing USER1 and USER2's email addresses in < > - you should not enter them when using these commands)

Get-MailboxFolderPermission -identity <USER1'S EMAIL ADDRESS>:\contacts
Get-MailboxFolderPermission -identity <USER1'S EMAIL ADDRESS>:\calendar

Now give USER2 permissions to those folders (in this example, USER2 is getting "editor" rights):

Add-MailboxFolderPermission -identity <USER1'S EMAIL ADDRESS>:\contacts -user <USER 2's EMAIL ADDRESS> -accessrights editor
Add-MailboxFolderPermission -identity <USER1'S EMAIL ADDRESS>:\calendar -user <USER 2's EMAIL ADDRESS> -accessrights editor

If you need to update USER2's permissions in future, replace add with set as shown (the permissions have been changed to "author" rights):

Set-MailboxFolderPermission -identity <USER1'S EMAIL ADDRESS>:\contacts -user <USER 2's EMAIL ADDRESS> -accessrights author
Set-MailboxFolderPermission -identity <USER1'S EMAIL ADDRESS>:\calendar -user <USER 2's EMAIL ADDRESS> -accessrights author

The Microsoft KB article detailing these commands and permissions are located at: https://technet.microsoft.com/en-us/library/dd298062(v=exchg.160).aspx