By far the simplest method is just using a serial null-modem cable plugged into an online PC. If you have a PC running Linux/Unix/BSD or a Mac you can connect with a small program called MultiLink.
This is what's involved: The Amiga and PC are connected via the serial cable. A small command is installed on the PC side and can be run from startup so it's always ready to accept the Amiga's connection. On the Amiga side you open a Terminal program and establish the connection with the PC. You run the Multilink program on the Amiga, and you can close the Telnet program. You now have a fully working internet connection using the PC's TCP/IP stack rather than running one on the Amiga.
The connection is surprisingly fast, faster than a 56k modem really, completely acceptible for browsing the web, chatting on IRC or even running a VNC client, having your PC's desktop (and modern browser) accessible in an Amiga window or screen, multitasking away with your other applications.
Check it out:
http://aminet.net/package/comm/net/mlink132
