One thing I would highly suggest is save any important PMs you do not want to disappear. Testing has not be finalized on PM messages. This is just cautionary advice.
You have 3 options to export your PMs
1) Export to CSV (comma separated value)
2) Export to CSV (Microsoft Excel style) (comma separated value)
3) Export to XML
On the bottom of each page of your Inbox and Sent Messages, there is a button to Export This View.
You do not have to select any messages. All messages on the PAGE will be exported automatically. You will have to export each page separately.
For me, the XML option allows for easier reading.
If you want to save your sent PMs, you will need to also export each page of those as well.