All platform members can add checklist tasks to an element (even if this is just within their own private grids in their own private folder area - for user and external member types).
For free accounts, an architect or builder can can add checklist items in the main grid library.
For professional and enterprise accounts, configurable access control will determine who has the access permission to add checklist items in the main grid library; see What is configurable access control?
Within a checklist area, you can add checklist items by clicking “Add a new checklist item +” and typing in the new task description.
You might just want to add a simple, single “Element completed” checklist item or, as in the example below, a series of related steps.
It is also possible to import a previously developed checklist from another element by clicking on “Add an existing checklist +” and selecting from the dropdown list (presented by grid name | element name | checklist area name).