Depends upon the type of networking. If you're simply after a fast internet connection, there are several tcp/ip stack programs available. The oldest is AmiTCP, for which you'll need to either manually configure or use a separate config program. Genesis is a program built into OS3.9 which has a custom wizard gui for AmiTCP and works pretty good and is fairly fast.
Other gui-configurable tcp programs include Miami and TermiteTCP. Miami or Miami Deluxe are available from Aminet but they're no longer registerable and the demo for each times out every 30 minutes. Then there's TermiteTCP, also no longer produced, but may be still purchaseable. The best bet speed wise and support wise is probably AmiTCP either through Genesis or some other configuration program. I'd personally recommend buying an OS3.9 CD as you'll get Genesis (and AmiTCP) built in and a nicer Workbench. It installs from CDROM and you already have the 3.1 roms and a Blizzard so it should run fairly well.
Download the latest versions of Ibrowse for the web and YAM (Yet Another Mailer) for email. There are many other programs available for download as shareware or freeware (e.g. ICQ, IRC - Wookiechat, etc.). Browsing may not be so great but it's serviceable and the other apps actually work surprisingly well and quickly.
To network the Amiga to a PC, there are several options. Samba is one such program and there may be others but I can't recall atm.