Wired Equivalent Privacy (WEP) is a largely deprecated form of wireless access point (AP or WAP) security. A number of security vulnerabilities have been found, allowing users to crack WEP keys in as little as under 60 seconds. Still, some administrators choose to use WEP because it provides an easy deterrant for non-technical users. WEP requires only a single, pre-shared key either in hexadecimal or plaintext.
Wi-Fi Protected Access (WPA) followed up WEP as a solution to WEP's many security flaws. WPA2, the second generation of WPA, has largely replaced the older protocol and implements a number of new algorithms and security features that were lacking in the first generation. Standard WPA/WPA2 methods require a pre-shared hexadecimal key, just like WEP, or a pre-shared passphrase. WPA has been extended in a number of ways to provide more secure enterprise-level access methods.
Sometimes you will see networks with the Extensible Authentication Protocol (EAP) prefix connected to Transport Layer Security (TLS) or prefixed by Lightweight (LEAP). This is an authentication framework that has been adopted by WPA and provides an additional layer of security on top of the passphrase or pre-shared key, establishing an encrypted tunnel to an authentication server. Depending on the administrator's specific set up, you will need to have an Identity, such as your corporate account name, password, and possibly an encryption certificate.
Protected EAP (PEAP) is the most commonly used implementation of the EAP standard with WPA for corporate networks. This requires a user identity and password like most EAP implementations, but further secures the communication by encrypting all handshakes. Many corporate networks allow users to connect to a PEAPv0 (EAP with MSCHAPv2, a common hash algorithm used with Microsoft Windows), without a certificate. The network will then require the installation of an access control client, like Cisco Clean Access, that will make sure that all necessary software is installed on a user's machine.