All of the setups below use ethernet cards (network cards) to connect you somehow to the Internet. That is why first we need to check if your ethernet card is working and most importantly can be used (read is supported) in Linux. There is a comprehensive Ethernet HOWTO at http://sunsite.unc.edu/LDP/HOWTO/Ethernet-HOWTO.html if you would like to read it otherwise try this.
Boot into Linux, During boot up a message like this should appear...
eth0: 3c509 at 0x300 tag 1, 10baseT port, address 00 20 af ee 01 23,
IRQ 10.
3c509.c:1.07 6/15/95 becker@cesdis.gsfc.nasa.gov
If you missed it type dmesg.
If you see a message like that you are set and you can go to the next section. If you can't see a message like this there are two possible explanations, your ethernet card is PNP (plug-n-play) and you need to use tools such as isapnptools to get it recognized (I am not quite sure on this because I don't have a single PNP card so correct me if I am wrong). The other explanation is that you need to set up your card.
Most cards today come with DOS programs that are used to setup your card. For example to get my 3COM 3c509 to work all I needed to do is boot into DOS and use a utility to configure my card. There is usually a Auto Configure option. If that does not solve your problem try changing the IRQ for the card using the same utility. I find that usually IRQs 10,11 and 12 work well. If none of this solves your problem please read the Ethernet HOWTO referenced above or post to a newsgroup such as comp.os.linux.setup or comp.os.linux.networking.