I also have a Thinkpad R31.
You need two things:
Hardware: A CD-writer or DVD-writer. You may have one of these already built into the laptop case.
Obviously a CD writer can only write CDs (up to 700 Mb) whereas DVD writer can write to DVDs (up to 4.7 Gb)
Software: You need some CD or DVD writing software. My R31 came with a program called Record Now which is very basic.
You need something like Nero or Roxio which have more features.
Once you have your CD/DVD writer, and CD/DVD writing software, you are ready to go.