How do you hook up to PS3 internet without Ethernet cable?

The PS3 can only be connected to the internet 2 ways. One is a Wired Connection with an ethernet cable and the other is with a WiFi signal from a broadband DSL or Cable modem. Routers are not expensive and are a one time cost often less than the cost of a PS3 game. The cost for your internet service provider is often the same amount every month.

Use the new free connectify software and install on PC and after that it will do everyhing and then you can go ps3 network settins and connect to the connectfy and that way you can share the PC internet with the ps3 without buying any routers which are very expensive

You really have not explained how you got the internet service for the PC. Sure Connectify claims that it "Transform your Windows laptop into a Wi-Fi hotspot at the click of a button so you can share a single Internet connection with your friends, co-workers, and mobile devices." They just don't say that they will enable you to connect and play your PS3 without any service interruptions see related link