Typically, if your Axim sees a wireless network, a window will pop up on the Today screen asking if you want to connect and if it connects to "The Internet" or "Work." For most public networks, it will not matter which of these you select ("Work" typically is best for home or corporate networks if you'll want to access shares or use ActiveSync on them). Once you connect, if it's a for-pay service, when you open internet explorer, it will ask you for your login information or a credit card.
Check the
Windows Mobile 2003 Second Edition section of the WiFi Guide for more information.