OK - there are several configuration items that need to be addressed first if you have not already done so. First, the appropriate permissions should be granted to the Portal User by using the Admin button and Manage Portal Roles. If there is not already a role there then create a new role. Grant permissions for a project to the portal user.
Once this is done then go to the Projects tab and add a new project (or use the List link and select an existing project). Next select the gray Accounts Tab under Projects. Use Link an Account and select the portal user's account. After this, go to the gray Team tab and select Modify Team. Search for the Portal user's account and select the contact(s) you want to add. Update the team and change the role of the new team member so that he has the appropriate permissions to add a ticket. The permissions for the various roles are customizable and can be modified for all members in that role by changing them under the Setup tab using Configure Permissions. By default, an observer can add a ticket, but only a contributer can modify it.
Hope this helps.