Breaking any encryption involves knowing a few things. First, you have to know that there is an encryption scheme. Secondly, you must know how encryption works.
Step 1
First you will need a to get some basic computer skills and a packet sniffing program compatible with your Operating System.
Step 2
Some packet sniffing programs are kismet, Airsnort (sniffs and cracks WEP), and airodump-ng(included in the aircrack-ng). I would recommend using aircrack-ng.
Step 3
Set up a wireless access point to use in this experiment, preferably one that you created. Otherwise, you will need the network administrator's agreement.
Step 4
Allow the packet sniffer some time to get a good sampling of the WEP encrypted packets. In other words, you have to give the program something to work with and match. This may take some time depending on your wireless card. Aircrack-ng has a program to speed this up by doing packet injection.
Step 5
Decipher the Public/private key by matching their packets for similarities.