If you need to give auser access to users calendar, based on if there are member of an group, this is the way.
Start Exchange Management Shell
$users = Get-ADGroupMember [groupname] | select -ExpandProperty name
foreach ($user in $users) {
$Mailbox = Get-Mailbox $user
#The Calendar, is name "Kalender" in danish
add-MailboxFolderPermission -identity “$($Mailbox.Name):\kalender” -AccessRights Editor -User [username]
set-MailboxFolderPermission -identity “$($Mailbox.Name):\kalender” -AccessRights Editor -User [username]
#English calendar
add-MailboxFolderPermission -identity “$($Mailbox.Name):\calendar” -AccessRights Editor -User [username]
set-MailboxFolderPermission -identity “$($Mailbox.Name):\calendar” -AccessRights Editor -User [username]
}