Choose appropriate plastic wrap. Look for wrap that's thicker than kitchen cling wrap. Consider purchasing a large roll of professional-grade shrink wrap.
Fold the plastic sheet to make a pocket for a CD. Professional plastic is already folded into half, but it's not difficult to do yourself.
Heat a seam in the plastic to fuse the two sides together. Professional heating elements allow you to simply pull down a spring-loaded arm to seal the plastic together and automatically separate the excess plastic. If you don't have access to a professional heating element, use a soldering iron.
Remove the excess plastic from the loosely shrink wrapped CD. If your heating device doesn't make it easy to simply pull off the excess material, snip around the border of the CD with a pair of scissors.
Turn a hairdryer on high. Wave the dryer over each CD is a smooth, back and forth motion. The plastic will shrink around the CD. Spend a little extra time on the edges to flatten the seams. Be careful not to hold the hairdryer in one place for too long, or the plastic will shrink too much and create a hole.