Not only is ``Dialup Networking'' available under Linux, it's also more stable and quicker. The name of the game is ``PPP'', the protocol employed for connecting to the Internet using modems. All you need is a tool that dials out and makes the connection.
To retrieve your mail from the ISP's server you need a tool called ``email fetcher'' that uses the POP protocol; when the mail is fetched it will appear as though it had been directly delivered to your Linux box. You'll then use a MUA (Mail User Agent) like pine, mutt, elm or many others to manage it.
While under Windows the dialer is automatically invoked when you launch an Internet application, under Linux the path is the other way round: you dial first, then launch the application. A thing called diald provides the usual behaviour. Installing and configuring dialup networking used to be one of the most difficult things to do under Linux, but not anymore: please consult the Configuration HOWTO.
Finally, a word about ``Network neighborhood'': you can make your Linux workstation appear as Windows NT/9x in a local network of Windows machines! The magic word is Samba: not the lively Brazilian dance, but an implementation of the SMB protocol for Linux. Go to http://samba.anu.edu.au/samba.