Users by default should have Internet access. Something is misconfigured. In what way do things "not work"? What are the error messages?
But really, the most important thing is: please, please upgrade your Fedora. Fedora 14 was just released yesterday, and it's a great, solid release with a lot of polish. Meanwhile, Fedora Core 6 was end-of-life December 7th, 2007. The older software, including Firefox, contains some serious bugs which make it not safe to use on the Internet.
In general, Fedora releases have a lifespan of 13 months and should be upgraded at least every second release. If that doesn't work for you, please, please use CentOS (based on RHEL5) or Ubuntu LTS (the LTS designates a special "long term support" release).
And as a plus, the problem you're having will almost certainly go away with a clean new install.