If you have room for a laptop to sit nearby while you're doing the show you can set it up and connect a microphone to it, recording everything you say at the same time it goes over the air. You'd just have to turn on/off two mics instead of one. Basic mics, such as this one can be found for $20. You can then use a free program such as Audacity to make the actual recording, with tutorials available on their website.
Another option is to purchase a digital voice recorder with a data port. Instead of recording in analog format to a tape it records it digitally as an audio file. When you're done you can take it home and simply connect the device to your computer and transfer the file over. They can be found for $40 on up at most electronic stores, with this model from Olympus being one of the latest and greatest. Just make sure it mentions being able to transfer the files to your computer, usually over USB.
Hope this helps,
I do a local radio program in my town and while on the air I would like to be recording the show. Other than going out and purchasing a tape recorder, is there any way that I could just record it on my computer.
What sort of external equipment will I need? What sort of cost is involved?
Also, please give me a step by step instruction on recording if possible, as I'm not computer savy.