Burning: the process of creating a CD/DVD - the data is "burned" onto the blank disk.
Ripping - taking the data from a CD/DVD and putting it onto another medium - eg taking a songs from a CD and saving them as MP3.
AheadNero is a good program for the burning process. It, or Roxio, may have come with your machine. Neither are free, but do come bundled with hardware.
DVDs cannot simply be copied - they need to be decoded into another format first. CDs can be copied directly if you have the permission of the copyright owner.