To create an assessment is necessary to have create permissions over the assessment instance. This permission can be inherit or can be granted by a site-wide administrator. This permissions can be managed by the site-wide administrator following the Permissions link in the assessment admin page.

To create triggers is necessary to have admin permissions over an assessment. The admin permission is inherit to the user that creates an assessment and also can be granted by the assessment administrator. This permissions can be managed follogging the Permission link that appears in the list of assessments.

Both links will lead the user to a page where the necessary permissions can be set.

Also the user can search for another user to manage his permissions:

After clicking OK, the user will appear in the list the permissions can be set properly.