The best easy-to-use but nevertheless quite professional software out there is Audacity.
It is cross-platform, that means that it's not OS-dependent: you can get a version of it for Windows, Mac OS X and GNU/Linux too.
Believe me, unless you have very unusual needs, you'll be ready to get started immediately:
press REC to record, STOP to end the task, SAVE the project or EXPORT him as MP3, WAV or Ogg Vorbis. End of story.
Once you get more confident with it, you can do a lot of stuff without having special skills:
- record multiple tracks (automatically, it creates a new track everytime you press Stop and Rec again), that you'll be able to mix down in a single one or to manage individually, according to your needs;
- apply tons of effects (fade in/fade out, filters, normalize, reverse,..);
- set ID3 Tags (meta-informations about Author, Title, Year, Genre,..)
- synchronize tracks, generate noise and so on...
NOTE: If your system is playing, but your Audacity is NOT recording, you should check your INPUT AUDIO SETTINGS, and verify that Recording Control and Stereo Mix are both enabled.
To open Input Audio Settings:
- Open your "Master Volume" window by double-clicking the speaker icon in the System Tray area (or through the Control Panel, Sound and Audio Device Properties, Volume, Advanced tab);
- Click on Options menu, select Properties, drop down the combobox and select your Input peripheral (every soundcard has integrated an input and an output device);
- Click ok and adjust the settings until they're good (recording volume affects the quality of the registration, so raise or lower it to an appropriate value).