One of the first things people ask me after the transition to Exchange 2007 is "How can I add some permissions to the user's mailbox?" There are a lot of documents on Microsoft's TechNet for Exchange 2007 but sometimes it makes you confused trying to find simple commands in all those documents.
So here is the command you use to add mailbox permissions:
Add-MailboxPermission -Identity "Some User" -User DusanK -Accessright Fullaccess -InheritanceType all
To this point everything is more or less clear but people find it hard to find more parameters for -Accessright, which is actually the most important part of the command. Here they are: