What is the best way to make two computers use the same internet connection?
 

I'm not sure how to do this, I have one computer that has an internet connection, just an ethernet card connected to a router.

I also have this other computer, which does not have internet access and it has an ethernet card.

Now I also own a switcher and two cables. Is it possible to get an internet connection running on both computers with this stuff? Or do I need to buy some more stuff to get it working like another ethernet card?

If you have a router and it has more than on port you can just plug it in there.

Otherwise you will need to do IP masquerading.

Do a google search to find out how to do this.

You could also try using the squid proxy program instead of ip masquerade that usually comes with redhat.

i think, using a squid proxy is a better option than ip masquerading.
squid proxy is a powerful program.it gives u a lot of control over u r connection.
search for information on squid.really good software..

I found IP masquerading to be nice and simple but I haven't tried Squid so I can't compare it. Have a look at this howto for setting it up.