There are a few options here;
The simplest is to get a 'crossover' cable, this is the ethernet version of an old serial null-modem cable (that's showing my age!). If you connect the 2 computers network cards with this and then configure them both with suitable IP addresses then they'll talk to each other quite happily.
The next option is to use a hub/switch and some normal network cables and to hook the machine up in much the same way as above, but with the hub joining the cables together. There's no real advantage to this over the crossover cable for just 2 computers, it only comes into it's own when you have more than 2 items that need to be networked.
The 3rd option is to go wireless - you add a wireless hub to the main computer (yours) and a wireless network card to your dad's and they can be connected together as if they were physically cabled up. I've not played with wireless yet so I'm no expert, but it's main advantage is obiously that you can have computers spread around the house without the wires running everywhere.
I'd personally recommend the crossover cable, it's cheap, effective and simple. You can share printers, files and internet connections without any problems and it's also quick and easy to unplug and store if you don't want a permanent setup.
Here's an example of some that are available.