You don't use a modem for dial-up - at least mine didn't! I had dial-up for a long time because that's all that was available here, but I finally got high speed internet through the same company when it was available. And I didn't have a modem until they came to install the high speed internet. My house is super-old with only one phone jack in the whole house, in the living room. When I had dial-up I had just a regular phone cord that plugged into the jack, then it had a splitter with two lines coming off of it - one going to the computer and the other one going to my land line phone. The one for the computer plugged directly into the back of it. It was extremely slow and when I was on the computer the phone didn't work - people just got a busy signal. I installed a program that would put up a screen on the computer that would give the Caller ID info when a phone call was trying to come through. From that screen I could choose to answer the call, ignore it, ask the caller to leave a message, etc. If I wanted to take the call, it would cut off the phone connection to the computer and I would have to redial to get back on the internet.
I was so glad to finally get the high-speed internet that I would NEVER want to go back to dial-up again. And I don't have to worry about possibly missing phone calls now. And some things I almost couldn't do with dial-up, like watching videos, because it was just so darn slooooow, it took forever for them to download. I actually could have got the high speed sooner but it's all through our local phone company and before, you had to get it in a 'packaged' bundle with the phone, internet, and satellie TV and I would have had to change to another satellite provider which I didn't want to do. As soon as they dropped the requirement to bundle with the TV, I jumped all over it!