To download all comments in a project, click on your company name in the list in your top left corner.
After that, click on the project you wish to download the comments from.
Then head to the context menu as pictured below and select "Download all comments".
This will download a .csv format file to your downloads folder.
Company and Project Administrators can also download a CSV file of all deleted comments for a project by clicking "Download all deleted comments". 
Please Note
Data -> From Text/CSV functionality in Excel to get a working data-table.