Microsoft Outlook has default email archiving capability. Check the link below which provides a detailed step by step way to archive the emails within Outlook.
http://email.about.com/od/outlooktips/qt/et_archive_mail.htm
But having said this, it doesn’t mean I recommend anyone to use the default Outlook Email Archiving feature. Though its a out of box solution which comes as part of the user Microsoft Outlook licensing it has its problem. Though the choice is completely on the user, I would take next couple of paragraphs to list out my criticism of the entire Outlook Email Archiving solution.
One of the first point I would like to bring is the storage technology that is used by Outlook. The Outlook creates another PST file for the archived emails. The emails are deleted from the original PST file. All these happens without any notification to the end user. It was shocking experience for me when I did it first time. There were many surprising things that happen.
Once the archiving completed. There archive pst is loaded on the Outlook. If the user have to search fro something in the email archive they have to first select the archive pst file and then perform the search. This is where the email archiving vendors make the task easier for the end user. Even though Outlook have such solution but I always would recommend to look for 3rd party email archiving solution.