Firstly, Never use public access points without WPA2 encryption!!!
If you are infected (on Windows), and assuming that the infection hasn't disabled stuff, you could try running this in a command window (start->run->cmd)
it should hopefully return a list of listening and active tcp/udp ports and remote addresses.
No one nowadays wants to infect your machine and not be able to communicate with it, either to control it or to siphon information from you, so this command is quite revealing, though it only shows active connections, and you might have a hard time deciphering and resolving the addresses, so shut down all other active programs such as skype first, which usually has loads of connections open.
If they only communicate once a day, then you might miss it.
Many viruses now block access to sites such as http://housecall.trendmicro.com which is a good first port of call for a scan. If you can't reach it then you are almost certainly infected with something.
Currently a nasty root kit is going around called TDSS or TD4, very difficult to remove but kaspersky.com has some useful information about it.
I don't have or use any antivirus for a decade and don't get infected.
Keep windows up to date, run behind a real firewall, don't click on unknown links or answer questions that lead to unreputable sites, and don't install stuff you can't be sure about - especially antivirus programs!
I recommend using Firefox or Chrome instead of IE, but any are OK as long as they are kept up to date.