Configuring internet connection sharing in GNU/Linux normally involves modifying several configuration files and issuing several commands. You need to at least:
This is definitely not user-friendly for beginners or for those who just want to set up a simple network.
Luckily, since version 0.7 of NetworkManager [projects.gnome.org], shipped with Ubuntu 8.10 and later, includes a very simple GUI for you set up a simple NAT network.
Suppose that you want to set up the following network:

Note that only the interface highlighted in green needs to be configured in a special way. It can be either wired or wireless. To let NetworkManager to manage the interface, edit the IPv4 Settings of the interface and set 'Shared to other computers':

That's all!
There are some limitations with this simple method. For example, the interface does not yet provide you to manage the addresses of the DHCP, or to configure the server as a bridge instead of setting up a private network. You have to edit a few files to do this, or to wait for NetworkManager to become more mature. Nonetheless, this simple feature provided is sufficient for configuring a simple network and meets the needs of most users.