Step 1: Place Bananas in Bag
Step 2: Remove Excess Air
Step 3: Seal Bag Closed
Helpers have suggested using a Ziplock (tm) storage bag as an alternative. In that case, press out the air and conform the bag to the banana(s) with the bag almost completely closed. Then, finish the closing process.
Step 4: Refrigerate Bananas
Step 5: Refrigeration Duration
If the bananas are pretty green when first subjected to the process, they can last the longest.
The picture was taken by a helper who refrigerated the banana for a week.