Here is a short tutorial on how to export WordPress comments to an excel .xls file, but you can also export them to PDF, Word or some other file type if you want.
You can export your comments either through the phpMyAdmin which most web hosting providers today have or by connecting to your MySQL server some other way and using a SQL query. The both are nothing else then just exporting the wp_comments table to a file
In both cases you will need to have a username and password for your MySQL server, to connect with.
There is also a plugin called Export comments to export comments to a csv file, which seems to be working with WordPress 3.4.2, but the file you get this way is pretty messy, you will get much more structured data by exporting directly from the MySQL.
Export through phpMyAdmin web interface
Connect to your phpMyAdmin and login with you username and password.
On home screen, click the plus sign by the database for your WordPress blog and select the wp_comments table. Then click on the export tab and select the format of the file you want to export to. Press the Go button and download the file to your computer. (The procedure might be a little different for you, depending on which version of phpMyAdmin you have installed)
You can then edit your .xls file further to contain only the information you need.