Ethernet cable/modem question?

Ok my mothers computer has a modem with the DSL and Ethernet cables and stuff to a modem to her computer. Do I have to have a modem for my computer as well. Or can I just plus an ethernet cable to a jack and into my computer?
Update: do I really have to buy something? is there a fast fix? I am trying to upgrade to Vista but my stupid wirless adapter from 2Wire is not compatible.
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