Instructions
Make sure you are in an area with Wi-Fi access. Most public locations will have a sign indicating this.
Turn on the PSP with no Universal Media Discs in the disk drive. Wait for the main menu to appear.
Push the Wi-Fi switch on the top edge of the PSP to the right. This will turn on the PSP's Wi-Fi capabilities.
Choose "Network Settings" on your PSP by navigating all the way to the left. Choose "Infrastructure Mode," then "New Connection," then "Scan." Choose the connection with the highest connection percentage (it will be at the top of the list), and press "X." At each of the following menu options, press the "X" button to choose the default setting. Unless you want to customize your settings, you will not need to alter any of the settings the PSP chooses for you.
Give your connection a name in the final screen so your PSP will remember the settings for future use. Then choose "Test Connection." If you get a "Successful" message, you can proceed to the Internet.
Repeat Steps 4 and 5 if you have a slow or weak connection, and choose a different hotspot if one is available.