A podcast is essentially nothing more than a big MP3 file, there are two parts to getting your podcasts out there: recording it and publishing it. Thankfully, neither is rocket science.
First as already stated, you need to record your podcast. You will need recording software and a microphone. You don't need anything fancy, cheap or even free software will do, e.g. magix music studio, Apple Garageband, Sony Acid Xpress (free), audacity (free). If you don't have broadband and don't want the hassle of downloading free software, but don't want to pay much either, look out for a magazine called Computer Music (or any similar home recording magazine), they usually give away free software on the coverdisc. Ideally get software that can record or export straight to MP3, it saves you the hassle of converting it from another format later.
When recording the podcast, you can assemble it digitally, by mixing MP3s onscreen, with your between song banter using the softwares audio editor. However its probably easier just to DJ using ordinary analogue equipment and record the output using the software all in one go, keeps things spontaneous too. All you need it some sort of preamp to take the input from your turntables/cd player/mike and plug the preamps output into your PC sound card input socket (tip: ensure line in selected and turned up on your computers recording volume). You can buy a pre-amp cheaply enough, but if you've already got a two (or more) channel mixer for DJing, that most likely has a built in pre-amp and will do just fine. Plug the output that normally goes to the PA into your soundcard, plug in your mic/turntables, hit record on the software and just DJ away.
The second bit is publishing your Podcast, you can do this via iTunes or another site like http://podcasts.yahoo.com and then just put a link to it in your blog. Or simply upload the file to some of your own FTP/Webspace (e.g. from your Internet provider, geocities or a paid hosting company) and link to that. Be warned though, uploading a podcast takes quite a bit of time, at decent MP3 quality, 1 minute of audio equates to about 1MB, therefore a 1 hour podcast may be 60MB. Forget it you're on dialup, it's ok on broadband but may take a while as the upload speed is usually about half that of your download speed.
Hope this helps!