OK just to get a better overall picture of your situation, do you have any WiFi network at home to begin with? You stated you don't have a router but does that mean you just don't have a separate, third-party wireless router you added yourself, or is it a matter where the modem your ISP sent you is just a modem and not a modem/router? Whatever the case, you do absolutely need to have a wireless router to have WiFi at home.
If it is a matter where you have a modem/router device from your ISP, the odds are on the side of the device itself there will be a label with various info printed on it, including the default SSID (the network name you'll see listed in your phone's Settings >> Wi-Fi menu) and password. You need to click on that entry and type in the SSID/password so your phone can from then on connect to your home network.
If it's a matter where you just have a modem but there's no router at all, you need to buy a wireless router, connect it to your modem, and then you can plug your computer into the wireless router and have your phone connected via WiFi. Then you'll have both your computer and phone able to have online access.