You need a few things
TCP/IP Stack.
Browser.
Email Client.
A Modem.
and a ISP other than AOL or MSN they run proprietery software.
You can get online with the basic Internet software that comes with OS 3.9, or you can purchase NetConnectIII CD it comes with a comprehensive list of Internet software for your Amiga.
try
www.thelist.com for a list of ISP's in your area. You don't need one that supports the Amiga all you need is one that lets you run your own software.
Amiga TCP/IP stacks include Genesis,Termite TCP,Miami,Miami Deluxe, The only one still available for retail purchase is Genesis
Browsers include Ibrowse,Voyager,AWEB
Email clients can be brought or downloaded for free Yam is agood example of a freeware Email client
I use Verizon DSL as my ISP.
For DSL or cable modems you will need an Ethernet card for your Amiga. to get one for your Amiga500 might be expensive you will need a ZorroII LAN Card and a slingshot or any other Zorro Expansion bus made for an A500.
Any Amiga with a graphics card would be better for internet surfing.
I use a Towered Amiga1200 with 060/PPC,193 Megs of RAM ,MediatorSX,Voodoo3 Graphics card,10/100 LAN card,Spider USB2.0 Card,Haupauge Win TV Card,ABIT AU10 Sound Card,Yamaha2100S CDRW, Pioneer DVD player,Wireless Keyboard and Mouse,19 inch Sceptre LCD Monitor.
I use my Amiga for surfing the net more than my PC.
Kurt
AWEB and Voyager still print better than IE and Netscape on my PC. On my PC the right 1/4 of the screen always gets chopped OFF.