If you want to configure who can administer asset, create new asset types and etc, you should configure permissions. Permissions are applied to Roles. If you aren't already familiar with Drupal's Role based permissions, please read Users, roles and permissions.

Asset module provides following permissions:

• Administer asset types (Create, edit and delete types of assets)
• Administer assets (Create, edit and delete asset entities)
• Access the assets overview page
• Access assets search widget (available only when asset widget module enabled)

Besides that Asset API uses 3 types of permission for each asset type:

1. Create asset
2. Edit asset
3. Delete asset

You can assign permissions to roles on permissions page (People > Permissions > Roles):

As a result, when user tries to do some action (for example, delete asset with certain type) which isn't allowed to his role, he will see Access denied (error 403) page: