How to crack a WEP wireless network ?

The basic idea is to capture enough packets. Each WEP data packet has an associated 3-byte IV (Initialization Vector). With enough packets captured (usually between 20k and 40k packets), cracking WEP is a non-issue.

First, you'd need to monitor traffic on the network by putting your network card in monitor mode and capture 20K+ data frames. This process can be very fast if your network card supports packet injection with a tool like aireplay-ng and an ARP replay attack.

Once the packets are captured, it is an easy task with a tool like aircrack-ng.

WEP can be easily cracked within minutes to a couple of hours, using WPA/WPA2 with a strong passprhase is much more secure (it can take days).

Note that cracking WEP requires simply capturing data. WPA/WPA2-PSK, on the other hand, requires capturing a handshake between a client and the access point, and then applying brute force dictionary attack.