The obvious thing that you'll need are some Compact Flash memory cards: they are your 'film' and the camera doesn't come with any. Go for ones with a decent capacity - at least 128Mb. Some sort of card reader for your computer is necessary, too. If you've got a laptop then PCCard adapters are very cheap and work well. If not, go for a USB card reader.
If your computer has a firewire port then you could transfer files direct from the camera. You'd need a suitable cable and the Nikon View software that comes with the camera to do this, but I have heard of people having considerable problems in this area so some form of card reader is likely to be a better bet.
You don't actually have to have any special software to use the D1, but if you want to use the RAW mode (something I'd urge you to try since it gives much better results than the JPEG and TIFF modes) then you need software to process the resulting NEF files. QImage and Bibble are both shareware so you can try them out to see which one you prefer before you buy.