How can recording a conversation that I personally am partaking in be illegal?

Where would I locate more info on this task?

It can vary from country/county to country/county. It can be OK, but in some places it would be a violation of the law. Check on the net or with the citizens info bureau or similar. Better safe then sorry.

Recording someone else without their permission can be considered an invasion of privacy, hence, some states, but not all, have sided with those who feel invaded in passing their anti-recording laws. The states which do allow recording without legal ramifications when only one party of the conversation agrees to be recorded are appropriately called "one-party" states. The recorder does not even have to notify the other party that she is being recorded, although businesses will routinely do so out of courtesy and to cover their ass, just in case some ignorant trouble-maker gets offended and uppity.

A Google search of telephone recording laws will reveal all. It's not that hard to locate more info.

Setting up a phone recording system is also not that difficult. It can be done with a simple tape recorder connected to your handset with a Radio Shack converter on the hardware side, associated with good Mac recording software. Programs like Sound Studio, Audio Hijack, maybe Audacity, and any number of inexpensive, one-trick ponies designed to capture "any" sound that comes into your Mac is all your need. You could even go higher end and use a dongle to capture the sound and process it well-designed logs.

Maybe even this software could do a good job. That you have to find out.

You do not really need to depend on Skype to capture the audio, although it's always nice to have several options to choose from.