For a start, a lot depends on your ISP. AOL for instance, has a shocking track record for Macs not connected directly to the web. Any form of connection sharing has, in the past, killed a connection dead before it even got off the ground with AOL.
Apple Mac OSX allows you to share an internet connection through any connectable interface.
In plain English that means you can set up your share to go through Ethernet, FireWire, AirPort etc.
Broadly speaking, this is what you need to be doing on the Mac:
Go to System Preferences.
Open the Network preference.
In the Network window, select the LAN connection you intend using, or from System Preferences select Sharing.
Click on the Internet tab.
Choose the connection that you’d like to share from or through.
Assuming you want to connect through the Ethernet port, select Built-in Ethernet.
You have a few choices here. Either you can more or less see how things go and try a web page request through your shared connection, or you can tweak how users share your Internet connection.
Whatever you do though, you kick things off by clicking the Start button to start sharing the Internet connection.
There’s a bit more to it but this is a brief overview and should be enough to get things going in the right direction. Note that the above steps apply to the OS version you specified. The steps are slightly (or very) different depending on which version of the Apple OS you are running.
POst back if you get stuck and I'll go into more detail.