Just FYI, there's already another thread going on this.
Just select the messages you want to save, then go down to the bottom of the page. On the right hand side there's a button that says "move to folder" with a bunch of options- delete, mark as read etc. It also says "download as xml", "download as csv", "download as text". Pick what you want, then hit the "go" button to the right of the selection and the selected PM's should download.
If you want to save everything into one file, you can highlight the entire page by clicking in the box at the top right showing the number of messages on the page.
XML was useless for me. CSV should open as a spreadsheet, that would make the document searchable later and the format is decent. Text is really basic, but the format isn't horrible and you could paste the text into a word processing document to search it later.