DOES WIFI CHARGE YOUR PHONE?

i have an lg incite. im not on an internet plan because at&t always has some secret charges that end up added to my bills. so i started using my wi-fi about 2-3 days ago. i go on myspace & myxer. im starting to dread my bill because im worried it will be high. so does using wifi cost you money if your using a wireless internet service in your house?