To export a project, select the "Export" drop-down in the upper right-hand side of the interface. It will give you the option to export your data in a number of different ways, including to a CSV (comma-separated value), TSV (tab-separated value), Excel, HTML table, or even to export the project as a whole.
Exporting the project as a whole would allow other individuals to upload the project into their own version of OpenRefine. This will copy over a list of any changes and transformations you performed and allow others to then pick up where you left off, something very useful for group work. When exporting the entire project, OpenRefine will prompt you as to whether you would like to download the project to your machine or save it to Google Drive. Exporting the spreadsheet as just a file will download directly to your machine.