The easiest way to record your show would be from within your encoder (if it supports this). Otherwise there are other methods like using a separate program like Audacity to record 'What your Hear' or 'Stereo Mix' which should be what your PC / Radio is playing. You could also use a stream ripper to rip your stream from the radio server but the quality of this method would be the same as your radio quality.
Depending on the encoder you use, we use Simple Cast, which has the facility to "record" your output to a log file. This is very useful. You can specify it makes a new file every hour etc so all your programmes are broken down into manageable chunks.