How do i set up a wireless router to my laptop?

So, I just bought a wireless-g adapter and the instructions are not helping me out at all. I have a laptop I am trying to get internet access on, and our home computer is a dsl cable modem. I am doing my best to follow everything its telling me to, but I cannot figure out how to get it synched up! Its difficult when no one in my household can help me, they are even more computer illiterate then I am. Advice anyone?! Did I even buy the right type of adapter?