A flash drive is pretty straightforward to use. You plug it into one of the ports on your computer that it fits into. (They'll be no mistaking which one it fits into. The only trick is to have it right side up. Usually the logo goes on the top.) Once it is plugged in, wait less than a minute and usually a window will open up. The window represents the storage space on the flash drive.
You can now click and drag whatever items (documents, photos, folders, etc.) onto the flash drive. This will bring a copy of the item onto the flash drive leaving the orginal item on the computer.
To safely remove the flash drive…If you're using an Apple, click and drag the icon that appeared on your desktop into the Trash. That will alert the computer that you want to remove the flash drive. It will not delete what is on it. If you're using a PC, look at the bottom right hand corner of the screen (near the time), there is a small green arrow symbol with a teeny image of the end of a cord (you'll never see that so look for the green arrow). Click on the green arrow and a small window opens listing any devices plugged into your computer (printer, flash drive, camera, etc.). Click on the one that isn't your printer and it is likely to be your flashdrive.
Having said all of that to instruct you on using the flash drive, this is not the best method fro transfering date from iTunes.
Are you listening to your music on an iPod or some other device? I recently wrote a blog on transferring music from and old computer to a new one: http://abbyandme.com/posts/an-easy-way-to-transfer-from-ipod-to-itunes. There are several programs like TuneJack on the web, but that's the one I am familiar with.
Obviously the one thing you don't want to do is to lose your music. So, be sure you have synced whatever device you listen to with your old computer so there is a latest version of your music on both the device and the old computer should something go wrong.
If all of this feels too overwhelming, you could recruit a high school student who has accomplished this task for themselves already. A plate of warm cookies, milk, and probably $10 can get the entire thing done. You also have th option of contacting Apple Service and Support at 1-800-275-2273.
Let me know how it works out.