Start Exchange Management Shell

If you want to export a user mailbox from exchange to a .pst file:
New-MailboxExportRequest -Mailbox daniel.andersson -FilePath \\exchange2010\export\daniel.andersson.pst

To see the status of the export:
Get-MailboxExportRequest -Name MailboxExport | fl

To see completed mailbox export requests:
Get-MailboxExportRequest | where {$_.status -eq “Completed”}

To clear all completed mailbox export request:
Get-MailboxExportRequest | where {$_.status -eq “Completed”} | Remove-MailboxExportRequest