I have a wifi question.?

My internet is currently with shaw and i want to learn more about wifi. I was told by a friend that if you get a Wireless-G Broadband Router and hook it up with you internet modem ..you will be able to get a internet anywhere in the house? My first question is ...is she rite? And also how does Wi fi work and do i just ask my internet company that i want to get wifi? I dont wann sound like an idiot... I live next to apartments and i usually just get internet for free for most of the time, but then it would all of sudden stop working..why? Is there anything i can get so the connection doesn't fade away (from the apartments)