I've used my A4000 with cable broadband and now DSL using a USB Ethernet adapter plugged into my Deneb.
I used Genesis off the OS3.9 CD (but I've also used AmigaKit's Easynet with a PCMCIA adapter on my A1200).
The only think you have to do is set certain values such as your IP address, subnet mask, DNS server, etc.
All of these values can either be obtained by speaking to customer sercices or (the really easy way), plug a PC into the modem/router, open a DOS window and type "IPCONFIG /ALL". Everything you need should be in the response (just change the last 3 digits of the IP address if the PC is going to stay connected: pick something like 195 which isn't likely to get automatically assigned).
Now, in the case of my DSL modem, I would have needed a PC to set that up first because I had to run software and enter my log-on and password into the modem to activate my account. No need for one now.