Step 1: Open the section you'd want to export the messages from E.g The SMS Received section.
Step 2: Check the messages to export by checking the box next to each (1). In case you'd want to select all of them, check the box at the top menu bar (2).
Note 1: For Windows users, ensure that the final names of the files downloaded always end with either .csv for csv exports, .xls for MS Excel exports or .vcf for vcard exports. This is because windows imposes a character limit on the names of files. The number of characters is calculated to include the entire pathname of the file on the computer. Another remedy to this is to ensure you do not store the export files in deep nested folders to ensure the resultant full path for the files does not exceed the limit. For reference the typical length of an export file from Frontline is 66 characters.
Note 2: For CSV format, if your contact data contains Non-English characters especially accent characters (such as é, ç, ü, etc) ensure that you open it with a spreadsheet application other than Microsoft Excel because Microsoft excel doesn't support CSV files with such characters. However, if you really want to use Microsoft Excel then it's better to download the XLS format instead.