With a dial-up service, your computer uses your home phone line to call a computer to get on the internet, therefore you need a home phone, and you will not be able to make calls on your home phone while you are on the internet.
There are many ISP's which provide this service, including MSN, AOL, NetZero, Earthlink, and many more. You should be able to find one for about $10 a month. After you find a service, they will provide you with instructions.