If you are using Nero software you should have InCD.
Put a blank CD/RW disk in and you will get a pop up window to format the CD. It will take about 30 to 40 minutes. Once that is done (and successful) you can use it just like a big floppy disk. Don't forget the computer you are transferring it to must also have a CD ReWriter drive and should be able to read it. If you are using Roxio software you should have DirectCD which does the same job.
Yes you can, Josquius, when you have the files, to be transferred, on your CD-RW or CD-R put that into the CD-ROM drive of the other computer and simply copy the files to the new computer. When the files have been transferred you might have to right click those files, choose Properties and change their attribute from "read only" to "archive". You certainly will have to do this if you use CD-R media.
Some CD/DVD combination drives (not writers) cannot read home-burned CDs.
I use Roxio Easy CD Creator and, so long as I close the CD so that it can be read on any machine (a tick-box option when you eject the CD after burning), I can then read the data on my CD-equipped laptop.