Skype can only be installed on the second-generation PSP (PSP-2000), and requires firmware 1.90, a Memory Stick Duo with 10MB free space and a Wi-Fi connection with Internet Access. Due to memory limitation in the first-generation PSPs (PSP-1000), Skype cannot be installed on these models. You can use your existing Skype account with the PSP or you can create a new one.
To Start using Skype, go to [Network] > [Skype]. You will need to either enter your existing Skype details or create a new account to use the Skype service. Creating a new account is easy, and can be done by following the on-screen steps. If you create a new account using your PSP, you can use the account on other devices that support Skype.