CiviCRM on Joomla: How to allow multiple users to add contcts, etc?
With CiviCRM on Joomla you do need to use the administrator backend for that functionality (unlike on Drupal). The frontend functionality is limited as you've discovered.

You can create a Joomla user group for these CiviCRM users and assign them the ability to login to the Joomla backend, but grant access only to the CiviCRM component. The steps would be something like:


Create a Joomla user group for these users, with group parent "Public" (Users > Groups > Add new group)
Give the group "Special" access (Users > Access levels, click Special) This step in setting up Joomla permissions doesn't make sense to me, but without it users will see an empty Joomla administrator dashboard - it's a bit of a gotcha
In System > Global Configuration, Permission tab: select the CiviCRM group and change "Site login" and "Administrator login" to Allowed
While still in the Permission tab, change from global to the CiviCRM component (select CiviCRM under COMPONENTS on left side) and grant permissions as required to the group (there are a lot of them)
Create users and add them to the group


Now this group will be able to log in to the Joomla backend but will have a limited menu (System, Components > CiviCRM, Help) like you see at http://joomla.demo.civicrm.org/administrator/

These are the basic steps to get you started; you can also look at using CiviCRM roles.