If a person attempts to start an assessment and gets a message "No skills assigned" - there can be 2 possible reasons and fixes.

About Gadget on a persons Summary page
Assessments tab on a persons dashboard  

1. The person has their Skill Set = role or team - however they don't have a role or team assigned 

In the above example - Skill Set = Role, however no roles are assigned.  We can edit the person to add a role.

2. The entity that the person has assigned as their Skill Set doesn't have any skills assigned to it

In the above example - Skill Set = Role and Role = "Customer Service", however the role does not have any Skill Categories assigned to it.  Simply edit the role to select the appropriate skill categories to assign to it.