Hi,
It depends a bit upon how you are connected to the Internet (cable, DSL, dial-up, fibre or mobile). Do you have a router (with a number of LAN Ethernet ports)? Please post back with additional information about connection method and equipment (and possibly the Internet service provider; do you mean EE in the UK?) to begin with.
If necessary, it is possible to make the iMac 'Wi-Fi capable' via an external wireless Ethernet bridge.
Also, do you have access to another computer at the same place (and do you wish to transfer files to that machine)?
You may want to have a look at the following articles to begin with,
http://support.apple.com/kb/ht1383
http://support.apple.com/kb/ts1317
Jan