Hello,
Skype is the most popular way to record interviews among podcasters. You will need a recorder since Skype doesn't have a recording option.
I like:
http://www.pamela-systems.com/
And I've also used:
http://hotrecorder.com/
Pamela has a lot more features than hot recorder. For example, she provides HTML template code for posting the recorded Skype audio and video calls as podcasts or blog entries. Very nice.
The pro version is only $24.95 and it's unlimited the cheaper plans limit you 30 minutes and they don't include all the goodies that the pro plan has so it's worth paying the extra $12. They also have a free version which limits your recordings to 15 minutes and it offers pretty basic features compares to pro. But you can give it a whirl for free before deciding if you like it and want to upgrade to pro version.
Hot Recorder is around $15. Not as much features and the recording is sometimes out of sync so for $10 more get Pamela.
If you don't want to use Skype you can use your phone. You will need a digital recorder (better than cassette) and a telephone recorder. I bought one from Radio Shack for $27. This is the that I picked up at Radio Shack. And I use an Olympus Digital recorder.
It's very easy you plug your phone via the adapter and then plug in the recorder to your digital recorder and that's it. Make your call, hit record and it will record your calls (both sides).
In my opinion these are the most affordable ways to record these interviews.