Assuming the card you refer you is essentially a 56k modem (and not a lan card, the steps are as follows:
1) get a TCP/IP stack: Miami or AmiTCP/Genesis will do. Search around for them (aminet etc)
2) install your stack of choice and set pcmser.device as your default device (in place of serial.device)
3) configure the stack with your ISPs settings (i.e. dial-up number, username and password)
4) click on 'dial' or 'go online' (depending on the stack) and that's it - you're online