Select your site so that the site information appears in the right panel
Click on the ‘Conversion tool’ located in the right panel
Begin Migration from your Site's Manage Site View
In the top right corner click settings
Select ‘Manage site’
In the Manage Site panel click ‘Convert to new Sites’
Upon initiating migration by one of the above methods, you will be brought to the 'Convert to the new Google Sites' screen. Below is an image of the 3 step process you will be taken through to convert your classic Google Site to new Sites.
Note: Depending on the size of your website, Step 2 (Draft Creation) may be quick or may take awhile to create the new Google Site draft. Please be patient until it has reached 100%. Upon reaching Step 3, it is beneficial to click on the 'Review draft' button so that you can view your migrated site.