you need a 3.5mm jack lead to g from your earphone port on your sterio walkman then the other end into the mic port on your comp and record it with soudforge then save it as a file thelead will cost you about 3 quid
there's 2 steps to this - not sure which one you're after so ill explain both:
Recording a mix:
Most DJ mixers will have a secondary output (usually called "record" or "booth"). This can be connected to your PC via an audio interface. A decent audio interface with the appropriate connectors can cost as little as £60 (try the Edirol range). Now you should be able to record your mixes onto hard disk with any audio recording application (wavelab and soundforge are the best). Make sure you get your levels just right cos you dont want any nasty clipping, try and peak at about -1db cos that'll give you a nice bit of headroom and you can maximise the volume of the mix later on if needed.
Getting it on the web:
Firstly, you'll want to encode it an an mp3 file, which will compress the file down to sensible levels, you can adjust all kinds of options during the encoding process, around 128kbps is near CD quality. The lower bitrate you use, the smaller the file will be, and the quicker it will be for people to download. Bear in mind, you can halve the file size by converting the mix to mono, and halving the bit rate. The bitrate is spread across both channels so a mono file at 64kbps will be the same quality as a stereo file at 128kbps. Once you have your file, you will need somewhere on the internet to host it, ask around your mates cos they might have some spare webspace for you... or you might be able to find some free hosting. Otherwise, Freeola offer unlimited webspace for a decent price. Next, you'll need an FTP program, which will upload your mix to your web space (your web space provider will most likely offer guides on how to do this).