You will first need to log into your Facebook account and click on the top right down arrow () which will open the navigation menu.
You will then have to click the Settings menu item.
The next page will show you your General Account Settings (in the middle of the screen).
At the bottom of this is a link to Download a copy of your Facebook data. You will need to click this.
After clicking the Download button, you will be given the option to Start the Archive. You will need to click the green Start My Archive button in the middle.
This will start the archive process which will (depending on how much Facebook data you have) take a while to process.
You will be sent 2 emails to the email address associated with your Facebook account.
The first email is just a notice to say you have recently requested a copy of your Facebook data. You can ignore this.
You will receive the second email when Facebook as finished collating all your data and your archive is available to be downloaded. You should click on the download link in the email, which will take you back to Facebook where you can start downloading your Facebook archive.
Once you have your Facebook archive, you want to double click on it which will open it up.
Navigate to the folder called html and once there select the messages.htm file and drag it onto your desktop.