Of course, if you don't have a TCP/IP stack and PPP client on the Amiga, you can just use regular terminal programs and Kermit/Xmodem/Zmodem for file transfer.
http://www.amigaforever.com/ae/ exists to make that easy...
If you have a network stack and want to bring the Amiga online, you just need a slipd or pppd and appropriate NAT or routing configured on the *NIX machine. As noted in another thread, I gather plip can exceed serial performance, but YMMV; start with serial first, and once you're confident about that fiddle with the more obscure arrangements.