How do I connect my ps3 to the Internet with out a computer?

"I don't have a modem" Well that's your problem right there. You need to call a local ISP and subscribe to some form of internet service.

If you don't have a modem then you cannot access the Internet, whether it's with a desktop computer, mobile device, PS3, or otherwise. Am I correct in understanding that you don't have Internet service at all? If that's the case you will need to find an Internet service provider capable of providing service to your geographic area. If you do pay for service but for some reason don't have a modem (perhaps you had one but it ceased functioning?) then you should contact your ISP for a replacement. There's a very good chance they'll give you a replacement for free. Once you have a modem you can go ahead and purchase a wireless router so that you can use your PS3 online. You will, however, need some sort of computer to set up the wireless network initially. You can use a laptop for this and you'll only need it briefly. After you successfully set up your wireless network you won't need the computer again until you need to make changes to the router configuration again.