Videos and collections can be moved from one project to another in two ways.
You can move a single item by clicking its title below the thumbnail in your dashboard, then selecting "Move to..." from its context menu.
You can also move multiple items at once by selecting them in the dashboard, then clicking "Move to..." at the top of your dashboard. You can even select multiple items at once from various projects.
You will then be prompted to choose your destination for the selected items. You can also create a new project as the destination on this screen from the + Project icon below the list of existing projects. Once your destination is chosen, click Move items.