Note: You can only move whole design files and not individual artboards. Please, upgrade to the Company plan to be able to move designs.
1. Select one or more design files
To select more than one file, just drag your mouse over the files, or hold the SHIFT key and select multiple files with your mouse.
2. Hit Move to …
Use the Move to … button in the contextual sidebar on the right.
3. Select a project or create a new one
Select any project from the list and press the button.
Move designs to a new project
Just select Move to a new project … below the button and create a new project.
NOTE: If you're in the Company plan or the Enterprise plan, you can also create subfolders in projects. Then you can move designs between projects and subfolders.