Search these Solaris forums, using keyword "8139".
There are more than 40 results on the subject.
(searching with keyword "realtek" gets you
more than 130 search hits, but not all of them
are related to your manufacturer's chipset.)
Then search these forums with keyword "internet".
There are hundreds of discussions about making a connection,
and many will help you complete your installation.
You may have to do some reading in those, to get a complete understanding.
The info is already here, so there's no sense repeating it over and over.