Well, to start with, you obviously need a modem. A stock 1200 can probably handle a 28.8Kbaud modem OK. To fully utilize a 56Kbps modem, you'll need a clockport serial card. Visit
Idividual Computers and look for the SilverSurfer in the Products section. If you happen to have broadband internet access, there maybe clockport ethernet adapters.
Once you have the modem (or ethernet card) in hand, a TCP/IP stack package is the next order of business. The only option I know of right now for Classic AmigaOS is a program called
GENESIS. As far as using this product, someone else will have to fill the breach. I use MiamiDeluxe.
The next item on the list is to procure a web browser. Here, you have some options: Aweb, IBroswse and Voyager.
Aweb recently went open source so if you have a buddy with a compiler, you can download the source and make it. I bought Aweb-II while I was still in the Marine Corps for my general usage. It has some javascript support and doesn't require Magic User Interface (MUI). Aweb-II v3.4SE is supplied with AmigaOS3.9.
IBrowse was the first browser I used. It uses MUI so you have to get and install MUI from Aminet or somewhere before you can use it. I used version 1.2 and had problems with it but v2.3 is the current release. From what I read, IBrowse has the best Javascript support among Amiga browsers.
Voyager is the other browser. I used this program once. However, many people have reported good results with later releases. As far as I know, this one also requires MUI.
There are a million and one other things in there but those are the basics.