My house has Broadband and a cable modem, but I think it only has one internet "out" plug.
First, check with the provider of the cable modem. Some of the new modems actually have WIFI in them, but it's turned off. I know someone who has "RoadRunner" or something like in Dallas and had WIFI and didn't even know it. So check that first. If you do have WIFI in your Cable Modem your provider should be able to help you set it with security features and such.
If your cable modem does not have WIFI built in, you will need to get a cheap switch. This will switch the "out" from your cable modem into 4, 6, 8 "outs", kind of like how a power strip splits power.
Then you can plug in an Airport Express into one of the newly created "outs". Follow the instructions that will come with the Airport Express and you should be up and running in no time.
For a more expensive option that will allow you to expand in the future get an Airport Extreme. This will basically do the same thing as the Airport Express and the switch combined. It will also allow you to share a USB device with your network, a printer, an external hard drive, etc. It will do those things along with providing WIFI for your home.