Explanation video: https://www.loom.com/share/33438b69d6bd46a2995c6312d5cdb024
Steps
Go to the Contacts page
Select the More Options button
Select Assign contacts to projects
You arrive on the Bulk Assign page
There is a column for each project and a row for each contact. Use the tick boxes to add/remove contacts to/from projects
Press Save
The assignments are done and you arrive back on the Contacts page