Visit an online musical instrument/equipment sales website such as americanmusical.com or musiciansfriend.com to research the recording equipment that will fit your needs. You will need to look for a portable solution that is not too complicated or bulky.
Recording software for your laptop will work perfectly for recording your live performance as long as you have the proper interface that allows the input of a hi-fi audio source. Your laptop must meet the performance requirements of the software. Avid's Pro Tools is the leader in recording software, and their Mbox makes their powerful software accessible to people from all walks of life. Also look into stand-alone multitrack recorders made by manufacturers like Boss, Tascam and Roland.
Read your owner's manual and master all necessary functions (record, play, rewind, fast forward, effects, inputs, etc.) before the gig. This will ensure that your recording goes smoothly without any interruptions in your live performance.
Run all microphone and instrument inputs through a mixer/PA system to simplify recording.
Adjust volume levels and EQ on the mixer and monitor the sound through studio quality headphones. Make sure that the volume and EQ levels are set in a way (not too high) that will eliminate distortion.
Run a cable from your mixer's output to your recording equipment.
Do a sound check by having the band play while the input levels on your recording equipment are adjusted. Make sure that the levels are set as high as possible without distortion. If you are in the band, you should be playing on the sound check. Have someone else adjust the input levels. Your missing instrument or voice will make it hard to adjust the levels properly, because once you are back in the mix, the added sound could cause distortion in the recording.
Have someone start the recording on your equipment (if you are in the band). Make sure they know what they are doing. You don't want to play a whole gig only to find out that you weren't recording.
Begin playing and recording your live music.
Stop recording and make sure that the music is saved when the performance is over.
Consult the owner's manual for your specific recording equipment to see how to edit and burn your saved music to CD.