How do I delete a password and reset phone with a new one?

I've had my moms old iPhone 3GS for about 6 mos. and I can't install apps because her username pops up and asks me for her password. I told her about it and she told me I had to get my own username and password because hers is still active with her current iPhone 4S. I just want to wipe her password clear and put my own ID and password on the device. I'm sure there is a way around this. Any suggestions?