This can be done with a couple of network cards and a network cable. Depending on your OS you can use either Windows "Internet Connection Sharing" or a third party proxy application.
You can do it, but I don't think you'd really want to. If both computers are using the connection simultaneously your download speeds will be painfully slow.
It's a dial-up so it already drags by like a gut-shot parakeet. We are both running 98SE. For the most part, the purpose would be so that if I am online downloading mp3s and my mom wants to check her email, I don't have to suspend the download and get offline. Just being curious, how is this done exactly?
With Win98 SE you'll have internet connection sharing. You'll need a network card in each machine and a crossover cable (Cat5 network cable) to connect the computers.