First, export the content on your current site. This can be All Content, or All Pages, Posts, Categories, etc. For this example, I am using the WordPress Importer to export All Posts.
1. In your WordPress Dashboard of the old site, go to ‘Tools -> Export‘.
2. Choose either All Content, Posts, or Pages. Leave other options as default unless you have other preferences. Click ‘Download Export File‘ to save the file. You are now done with your old site. You may logout.